Machine Reading Comprehension (MRC), which requires the machine to answer questions based on the given context, has gained increasingly wide attention with the incorporation of various deep learning techniques over the past few years. Although the research of MRC based on deep learning is flourishing, there remains a lack of a comprehensive survey to summarize existing approaches and recent trends, which motivates our work presented in this article. Specifically, we give a thorough review of this research field, covering different aspects including (1) typical MRC tasks: their definitions, differences and representative datasets; (2) general architecture of neural MRC: the main modules and prevalent approaches to each of them; and (3) new trends: some emerging focuses in neural MRC as well as the corresponding challenges. Last but not least, in retrospect of what has been achieved so far, the survey also envisages what the future may hold by discussing the open issues left to be addressed.