Emotion Recognition in Conversations (ERC) has gained increasing attention for developing empathetic machines. Recently, many approaches have been devoted to perceiving conversational context by deep learning models. However, these approaches are insufficient in understanding the context due to lacking the ability to extract and integrate emotional clues. In this work, we propose novel Contextual Reasoning Networks (DialogueCRN) to fully understand the conversational context from a cognitive perspective. Inspired by the Cognitive Theory of Emotion, we design multi-turn reasoning modules to extract and integrate emotional clues. The reasoning module iteratively performs an intuitive retrieving process and a conscious reasoning process, which imitates human unique cognitive thinking. Extensive experiments on three public benchmark datasets demonstrate the effectiveness and superiority of the proposed model.