The electricity market has a vital role to play in the decarbonisation of the energy system. However, the electricity market is made up of many different variables and data inputs. These variables and data inputs behave in sometimes unpredictable ways which can not be predicted a-priori. It has therefore been suggested that agent-based simulations are used to better understand the dynamics of the electricity market. Agent-based models provide the opportunity to integrate machine learning and artificial intelligence to add intelligence, make better forecasts and control the power market in better and more efficient ways. In this systematic literature review, we review 55 papers published between 2016 and 2021 which focus on machine learning applied to agent-based electricity market models. We find that research clusters around popular topics, such as bidding strategies. However, there exists a long-tail of research applications that could benefit from the high intensity research from the more investigated applications.