Chinese font generation aims to create a new Chinese font library based on some reference samples. It is a topic of great concern to many font designers and typographers. Over the past years, with the rapid development of deep learning algorithms, various new techniques have achieved flourishing and thriving progress. Nevertheless, how to improve the overall quality of generated Chinese character images remains a tough issue. In this paper, we conduct a holistic survey of the recent Chinese font generation approaches based on deep learning. To be specific, we first illustrate the research background of the task. Then, we outline our literature selection and analysis methodology, and review a series of related fundamentals, including classical deep learning architectures, font representation formats, public datasets, and frequently-used evaluation metrics. After that, relying on the number of reference samples required to generate a new font, we categorize the existing methods into two major groups: many-shot font generation and few-shot font generation methods. Within each category, representative approaches are summarized, and their strengths and limitations are also discussed in detail. Finally, we conclude our paper with the challenges and future directions, with the expectation to provide some valuable illuminations for the researchers in this field.