This study focuses on Code Generation task that aims at generating relevant code fragments according to given natural language descriptions. In the process of software development, developers often encounter two scenarios. One is writing a large amount of repetitive and low-technical code for implementing common functionalities. The other is writing code that depends on specific task requirements, which may necessitate external resources such as documentation or other tools. Therefore, code generation has received a lot of attention among academia and industry for assisting developers in coding. It has also been one of the key concerns in the field of software engineering to make machines understand users’ requirements and write programs on their own. The recent development of deep learning techniques, especially pre-training models, makes the code generation task achieve promising performance. In this study, the current work on deep learning-based code generation is systematically reviewed and the current deep learning-based code generation methods are classified into three categories: methods based on code features, methods incorporated with retrieval, and methods incorporated with post-processing. The first category refers to the methods that use deep learning algorithms for code generation based on code features, and the second and third categories improve the performance of the methods in the first category. The existing research results of each category of methods are systematically reviewed, summarized, and commented. Besides, the study analyzes the corpus and the popular evaluation metrics used in the existing code generation work. Finally, it summarizes the overall literature review and provides a prospect for future research directions worthy of attention.