Training machines to understand natural language and interact with humans is an elusive and essential task in the field of artificial intelligence. In recent years, a diversity of dialogue systems has been designed with the rapid development of deep learning researches, especially the recent pre-trained language models. Among these studies, the fundamental yet challenging part is dialogue comprehension whose role is to teach the machines to read and comprehend the dialogue context before responding. In this paper, we review the previous methods from the perspective of dialogue modeling. We summarize the characteristics and challenges of dialogue comprehension in contrast to plain-text reading comprehension. Then, we discuss three typical patterns of dialogue modeling that are widely-used in dialogue comprehension tasks such as response selection and conversation question-answering, as well as dialogue-related language modeling techniques to enhance PrLMs in dialogue scenarios. Finally, we highlight the technical advances in recent years and point out the lessons we can learn from the empirical analysis and the prospects towards a new frontier of researches.