Natural language generation has witnessed significant advancements due to the training of large language models on vast internet-scale datasets. Despite these advancements, there exists a critical challenge: These models can inadvertently generate content that is toxic, inaccurate, and unhelpful, and existing automatic evaluation metrics often fall short of identifying these shortcomings. As models become more capable, human feedback is an invaluable signal for evaluating and improving models. This survey aims to provide an overview of recent research that has leveraged human feedback to improve natural language generation. First, we introduce a taxonomy distilled from existing research to categorize and organize the varied forms of feedback. Next, we discuss how feedback can be described by its format and objective, and cover the two approaches proposed to use feedback (either for training or decoding): directly using feedback or training feedback models. We also discuss existing datasets for human-feedback data collection, and concerns surrounding feedback collection. Finally, we provide an overview of the nascent field of AI feedback, which uses large language models to make judgments based on a set of principles and minimize the need for human intervention. We also release a website of this survey at feedback-gap-survey.info.