Training machines to understand natural language and interact with humans is an elusive and essential task of artificial intelligence. A diversity of dialogue systems has been designed with the rapid development of deep learning techniques, especially the recent pre-trained language models (PrLMs). Among these studies, the fundamental yet challenging type of task 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 technical perspective of dialogue modeling for the dialogue comprehension task. 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. In addition, we categorize dialogue-related pre-training techniques which are employed to enhance PrLMs in dialogue scenarios. Finally, we highlight the technical advances in recent years and point out the lessons from the empirical analysis and the prospects towards a new frontier of researches.