Textual conversational agent or chatbots' development gather tremendous traction from both academia and industries in recent years. Nowadays, chatbots are widely used as an agent to communicate with a human in some services such as booking assistant, customer service, and also a personal partner. The biggest challenge in building chatbot is to build a humanizing machine to improve user engagement. Some studies show that emotion is an important aspect to humanize machine, including chatbot. In this paper, we will provide a systematic review of approaches in building an emotionally-aware chatbot (EAC). As far as our knowledge, there is still no work focusing on this area. We propose three research question regarding EAC studies. We start with the history and evolution of EAC, then several approaches to build EAC by previous studies, and some available resources in building EAC. Based on our investigation, we found that in the early development, EAC exploits a simple rule-based approach while now most of EAC use neural-based approach. We also notice that most of EAC contain emotion classifier in their architecture, which utilize several available affective resources. We also predict that the development of EAC will continue to gain more and more attention from scholars, noted by some recent studies propose new datasets for building EAC in various languages.