Artificial intelligence raises legal and ethical issues or risks when used to automated decision-making in areas closely related to daily life. Trustworthy machine learning is the core technology in artificial intelligence safety. It is a trending research direction, of which fairness is an essential aspect. Fairness is the absence of any prejudice or favoritism towards an individual or a group based on their inherent or acquired characteristics which are irrelevant in the particular context of decision-making. A comprehensive and structured overview of three research contents is provided, namely, fair representation, fair modeling, and fair decision-making algorithm. The potential causes and harmful consequences of unfairness are first identified in data and algorithm processing. Then, the abstract definition and primary mechanisms for eliminating unfairness are summarized. The research on fairness is at its early stage in fields such as computer vision, natural language processing, recommender systems, multi-agent systems, and federated learning. Fairness is a prerequisite for the application of machine learning, and constructing fair algorithms has theoretical significance and practical values.