Emotion is intrinsic to humans and consequently emotion understanding is a key part of human-like artificial intelligence (AI). Emotion recognition in conversation (ERC) is becoming increasingly popular as a new research frontier in natural language processing (NLP) due to its ability to mine opinions from the plethora of publicly available conversational data in platforms such as Facebook, Youtube, Reddit, Twitter, and others. Moreover, it has potential applications in health-care systems (as a tool for psychological analysis), education (understanding student frustration) and more. Additionally, ERC is also extremely important for generating emotion-aware dialogues that require an understanding of the user's emotions. Catering to these needs calls for effective and scalable conversational emotion-recognition algorithms. However, it is a strenuous problem to solve because of several research challenges. In this paper, we discuss these challenges and shed light on the recent research in this field. We also describe the drawbacks of these approaches and discuss the reasons why they fail to successfully overcome the research challenges in ERC.