Offline handwritten Chinese recognition is an important research area of pattern recognition, including offline handwritten Chinese character recognition (offline HCCR) and offline handwritten Chinese text recognition (offline HCTR), which are closely related to daily life. With new deep learning techniques and the combination with other domain knowledge, offline handwritten Chinese recognition has gained breakthroughs in methods and performance in recent years. However, there have yet to be articles that provide a technical review of this field since 2016. In light of this, this paper reviews the research progress and challenges of offline handwritten Chinese recognition based on traditional techniques, deep learning methods, methods combining deep learning with traditional techniques, and knowledge from other areas from 2016 to 2022. Firstly, it introduces the research background and status of handwritten Chinese recognition, standard datasets, and evaluation metrics. Secondly, a comprehensive summary and analysis of offline HCCR and offline HCTR approaches during the last seven years is provided, along with an explanation of their concepts, specifics, and performances. Finally, the main research problems in this field over the past few years are presented. The challenges still exist in offline handwritten Chinese recognition are discussed, aiming to inspire future research work.