Memory gives us identity, shapes our personality and drives our reactions to different situations in life. We actively create expectations, track the fulfilment of these expectations and dynamically modify our memory when new experiences demand it. Yet up to date, many important social aspects of human memory to artificial intelligent social agents have not been given much attention. Thus, this article is going to review on the current state-of-the-art of memory models for social companions, particularly on memory aspects that have been explored and proved useful and other potential memory aspects that would be beneficial if included.