Infectious diseases are caused by pathogenic microorganisms, such as bacteria, viruses, parasites or fungi, which can be spread, directly or indirectly, from one person to another. Infectious diseases pose a serious threat to human health, especially COVID-19 that has became a serious worldwide health concern since the end of 2019. Contact tracing is the process of identifying, assessing, and managing people who have been exposed to a disease to prevent its onward transmission. Contact tracing can help us better understand the transmission link of the virus, whereby better interrupting its transmission. Given the worldwide pandemic of COVID-19, contact tracing has become one of the most critical measures to effectively curb the spread of the virus. This paper presents a comprehensive survey on contact tracing, with a detailed coverage of the recent advancements the models, digital technologies, protocols and issues involved in contact tracing. The current challenges as well as future directions of contact tracing technologies are also presented.