Contact tracing is an effective method to control emerging infectious diseases. Since the 1980's, modellers are developing a consistent theory for contact tracing, with the aim to find effective and efficient implementations, and to assess the effects of contact tracing on the spread of an infectious disease. Despite the progress made in the area, there remain important open questions. In addition, technological developments, especially in the field of molecular biology (genetic sequencing of pathogens) and modern communication (digital contact tracing), have posed new challenges for the modelling community. In the present paper, we discuss modelling approaches for contact tracing and identify some of the current challenges for the field.