EntityFrameworkCore extensions:
-Bulk operations (Insert, Update, Delete, Read, Upsert, Sync, Truncate) and
-Batch ops (Delete, Update).
Library is Lightweight and very Efficient, having all mostly used CRUD operation.
Was selected in top 20 EF Core Extensions recommended by Microsoft.
Current version is using EF Core 3.1 and at the moment supports Microsoft SQL Server(2008+) and SQLite.
It is targeting NetStandard 2.0 so it can be used on project targeting NetCore(2.0+) or NetFramework(4.6.1+).
Versions between 3.1.0 and 3.0.0 are using EF Core 3.0 and targeting NetStandard 2.1 so could only be on NetCore(3.0+).
Versions before 3.0, last 2.6.4, are targeting NetStandard 2.0 and can be used with NetCore(2.2) or NetFramework(4.6.1+).
EFCore/v.Nuget: EFCore2.1/v2.4.1 EFCore2.0/v2.0.8, and for EF Core 1.x use 1.1.0 (targeting NetStandard 1.4)
Under the hood uses SqlBulkCopy for Insert, for Update/Delete combines BulkInsert with raw Sql MERGE.
For SQLite there is no BulkCopy, instead library uses plain SQL combined with UPSERT.
Bulk Tests can not have UseInMemoryDb because InMemoryProvider does not support Relational-specific methods.

Available on latest version.
Package manager console command for installation: Install-Package EFCore.BulkExtensions

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It's pretty simple and straightforward.
Bulk Extensions are made on DbContext class and can be used like this (both regular and Async methods are supported):

context.BulkInsert(entitiesList);                 context.BulkInsertAsync(entitiesList);
context.BulkUpdate(entitiesList);                 context.BulkUpdateAsync(entitiesList);
context.BulkDelete(entitiesList);                 context.BulkDeleteAsync(entitiesList);
context.BulkInsertOrUpdate(entitiesList);         context.BulkInsertOrUpdateAsync(entitiesList);       //Upsert
context.BulkInsertOrUpdateOrDelete(entitiesList); context.BulkInsertOrUpdateOrDeleteAsync(entitiesList); //Sync
context.BulkRead(entitiesList);                   context.BulkReadAsync(entitiesList);
context.Truncate<Entity>();                       context.TruncateAsync<Entity>();

Batch Extensions are made on IQueryable DbSet and can be used as in the following code segment.
They are done as pure sql and no check is done whether some are prior loaded in memory and are being Tracked.
(updateColumns is optional parameter in which PropertyNames added explicitly when we need update to it's default value)

// Delete
context.Items.Where(a => a.ItemId >  500).BatchDelete();
context.Items.Where(a => a.ItemId >  500).BatchDeleteAsync();

// Update (using Expression arg.) supports Increment/Decrement 
context.Items.Where(a => a.ItemId <= 500).BatchUpdate(a => new Item { Quantity = a.Quantity + 100 });
  // can be as value '+100' or as variable '+incrementStep' (int incrementStep = 100;)
  
// Update (via simple object)
context.Items.Where(a => a.ItemId <= 500).BatchUpdate(new Item { Description = "Updated" });
context.Items.Where(a => a.ItemId <= 500).BatchUpdateAsync(new Item { Description = "Updated" });
// Update (via simple object) - requires additional Argument for setting to Property default value
var updateColumns = new List<string> { nameof(Item.Quantity) }; // Update 'Quantity' to default value('0'-zero)
var q = context.Items.Where(a => a.ItemId <= 500);
int affected = q.BatchUpdate(new Item { Description = "Updated" }, updateColumns);//result assigned to variable

If Windows Authentication is used then in ConnectionString there should be Trusted_Connection=True; because Sql credentials are required to stay in connection.

When used directly each of these operations are separate transactions and are automatically committed.
And if we need multiple operations in single procedure then explicit transaction should be used.
For example since child tables are not automatically inserted with parent we need explicit second call:

using (var transaction = context.Database.BeginTransaction())
{
    context.BulkInsert(entitiesList);
    context.BulkInsert(subEntitiesList);
    transaction.Commit();
}

BulkInsertOrUpdate method can be used when there is need for both operations but in one connection to database.
It makes Update when PK(PrimaryKey) is matched, otherwise does Insert.

BulkInsertOrUpdateOrDelete effectively synchronizes table rows with input data.
Those in Db that are not found in the list will be deleted.

BulkRead does SELECT and JOIN based on one or more Unique columns that are specified in Config UpdateByProperties.
More info in the Example at the bottom.

BulkInsert_/OrUpdate/OrDelete methods can have optional argument BulkConfig with properties (bool, int, object, List):
{ PreserveInsertOrder, SetOutputIdentity, BatchSize, NotifyAfter, BulkCopyTimeout, EnableStreaming, UseTempDB, TrackingEntities, WithHoldlock, CalculateStats, StatsInfo, PropertiesToInclude, PropertiesToExclude, UpdateByProperties, SqlBulkCopyOptions }
Default behaviour is
{ PreserveInsertOrder: false, SetOutputIdentity: false, BatchSize: 2000, NotifyAfter: null, BulkCopyTimeout: null,
EnableStreaming: false, UseTempDB: false, TrackingEntities: false, WithHoldlock: true,
CalculateStats: false, StatsInfo: null, PropertiesToInclude: null, PropertiesToExclude: null, UpdateByProperties: null, SqlBulkCopyOptions: Default }

If we want to change defaults, BulkConfig should be added explicitly with one or more bool properties set to true, and/or int props like BatchSize to different number.
Config also has DelegateFunc for setting Underlying-Connection/Transaction, e.g. in UnderlyingTest.
When doing update we can chose to exclude one or more properties by adding their names into PropertiesToExclude, or if we need to update less then half column then PropertiesToInclude can be used. Setting both Lists are not allowed.

Additionaly there is UpdateByProperties for specifying custom properties, by which we want update to be done.
Using UpdateByProperties while also having Identity column requires that Id property be Excluded.
If NotifyAfter is not set it will have same value as BatchSize while BulkCopyTimeout when not set has SqlBulkCopy default which is 30 seconds and if set to 0 it indicates no limit.

PreserveInsertOrder and SetOutputIdentity have purpose only when PK has Identity (usually int type with AutoIncrement), while if PK is Guid(sequential) created in Application there is no need for them.
Also Tables with Composite Keys have no Identity column so no functionality for them in that case either.

var bulkConfig = new BulkConfig {PreserveInsertOrder = true, SetOutputIdentity = true, BatchSize = 4000 };
context.BulkInsert(entList, bulkConfig);
context.BulkInsertOrUpdate(entList, new BulkConfig { PreserveInsertOrder = true });
context.BulkInsertOrUpdate(entList, b => b.SetOutputIdentity = true); //example BulkConfig set with Action arg.

PreserveInsertOrder makes sure that entites are inserted to Db as they are ordered in entitiesList.
However for this to work Id column needs to be set for the proper order.
For example if table already has rows, let's say it has 1000 rows with Id-s (1:1000), and we now want to add 300 more.
Since Id-s are generated in Db we could not set them, they would all be 0 (int default) in list.
But if we want to keep the order as they are ordered in list then those Id-s should be set say 1 to 300 (for BulkInsert).
Here single Id value itself doesn't matter, db will change it to (1001:1300), what matters is their mutual relationship for sorting.
Insertion order is implemented with TOP in conjuction with ORDER BY. stackoverflow:merge-into-insertion-order.
This config should also be used when we have set SetOutputIdentity on Entity containing NotMapped Property. issues/76

When using PreserveInsertOrder with SetOutputIdentity Id value does matter.
If it's BulkInsertOrUpdate method for those that will be updated it has to match Id.
And if we need to sort those for insert(BulkInsert/OrUpdate) and not have conflict with existing Id-s, there are 2 ways:
One is set Id to really high values, order of magnitude 10^10, and another even better setting them to negative values.
So if we have list of 8000, say 3000 for update (they keep the real Id) and 5000 for insert then Id-s could be (-5000:-1).

SetOutputIdentity is useful when BulkInsert is done to multiple related tables, that have Identity column.
After Insert is done to first table, we need Id-s that were generated in Db because they are FK(ForeignKey) in second table.
It is implemented with OUTPUT as part of MERGE Query, so in this case even the Insert is not done directly to TargetTable but to TempTable and then Merged with TargetTable.
When used if PreserveInsertOrder is also set to true Id-s will be updated in entitiesList, and if PreserveInsertOrder is false then entitiesList will be cleared and reloaded.
Example of SetOutputIdentity with parent-child FK related tables:

int numberOfEntites = 1000;
var entities = new List<Item>();
var subEntities = new List<ItemHistory>();
for (int i = 1; i <= numberOfEntites; i++)
{
    var entity = new Item { ItemId = i, Name = $"Name {i}" }; //ItemId set by Db,here only to keep Insert order
    entity.ItemHistories = new List<ItemHistory>()
    {
        new ItemHistory { Remark = $"Info {i}.1" },
        new ItemHistory { Remark = $"Info {i}.2" }
    };
    entities.Add(entity);
}
using (var transaction = context.Database.BeginTransaction())
{
    var bulkConfig = new BulkConfig { PreserveInsertOrder = true, SetOutputIdentity = true };
    context.BulkInsert(entities, bulkConfig);
    foreach (var entity in entities) {
        foreach (var subEntity in entity.ItemHistories) {
            subEntity.ItemId = entity.ItemId; // setting FK to match its linked PK that was generated in DB
        }
        subEntities.AddRange(entity.ItemHistories);
    }
    context.BulkInsert(subEntities);
    transaction.Commit();
}

When CalculateStats is set to True the result is return in BulkConfig.StatsInfo (StatsNumber-Inserted/Updated).
If used for pure Insert (with Batching) then SetOutputIdentity should also be configured because Merge have to be used.
TrackingEntities can be set to True if we want to have tracking of entities from BulkRead or when SetOutputIdentity is set.
UseTempDB when set then BulkOperation has to be inside Transaction

SqlBulkCopyOptions is Enum with [Flags] attribute which enables specifying one or more options:
Default, KeepIdentity, CheckConstraints, TableLock, KeepNulls, FireTriggers, UseInternalTransaction

Last optional argument is Action progress (Example in EfOperationTest.cs RunInsert() with WriteProgress()).

context.BulkInsert(entitiesList, null, (a) => WriteProgress(a));

Library supports Global Query Filters and Value Conversions as well.
It also maps OwnedTypes, which is implemented with DataTable class.
With Computed and Timestamp Columns it will work in a way that they are automatically excluded from Insert. And when combined with SetOutputIdentity they will be Selected.
Bulk Extension methods can be Overridden if required, for example to set AuditInfo.
If having problems with Deadlock there is useful info in issue/46.

When having TPH (Table-Per-Hierarchy) inheritance model it can be set in 2 ways.
First is automatically by Convention in which case Discriminator column is not directly in Entity but is Shadow Property.
And second is to explicitly define Discriminator property in Entity and configure it with .HasDiscriminator().
Important remark regarding the first case is that since we can not set directly Discriminator to certain value we need first to add list of entities to DbSet where it will be set and after that we can call Bulk operation. Note that SaveChanges are not called and we could optionally turn off TrackingChanges for performance. Example:

public class Student : Person { ... }
context.Students.AddRange(entities); // adding to Context so that Shadow property 'Discriminator' gets set
context.BulkInsert(entities);

When we need to Select from big List of some Unique Prop./Column use BulkRead (JOIN done in Sql) for Efficiency:

// instead of WhereIN which will TimeOut for List of several thousand
var entities = context.Items.Where(a => itemsNames.Contains(a.Name)).AsNoTracking().ToList(); //SQL IN operator
// or JOIN in Memory that loads entire table
var entities = context.Items.Join(itemsNames, a => a.Name, p => p, (a, p) => a).AsNoTracking().ToList();

// USE
var items = itemsNames.Select(a => new Item { Name = a }); // creating list of Items where only Name is set
var bulkConfig = new BulkConfig { UpdateByProperties = new List<string> { nameof(Item.Name) } };
context.BulkRead(items, bulkConfig); // Items list will be loaded from Db with data(other properties)

Following are performances (in seconds for SQL Server):

TestTable has 6 columns (Guid, string, string, int, decimal?, DateTime).
All were inserted and 2 of them (string, DateTime) were updated.
Test was done locally on following configuration: INTEL Core i5-3570K 3.40GHz, DDRIII 8GB x 2, SSD 840 EVO 128 GB.
For small data sets there is an overhead since most Bulk ops need to create Temp table and also Drop it after finish. Probably good advice would be to use Bulk ops for sets greater than 1000.