Human–computer conversation has long been an interest of artificial intelligence and natural language processing research. Recent years have seen a dramatic improvement in quality for both task-oriented and open-domain dialogue systems, and an increasing amount of research in the area. The goal of this work is threefold: (1) to provide an overview of recent advances in the field of open-domain dialogue, (2) to summarize issues related to ethics, bias, and fairness that the field has identified as well as typical errors of dialogue systems, and (3) to outline important future challenges. We hope that this work will be of interest to both new and experienced researchers in the area.