Two-dimensional (2D) layered materials, including graphene, black phosphorus (BP) and transition metal dichalcogenide (TMD) such as molybdenum disulfide (MoS₂), tungsten diselenide (WSe₂), have attracted increasing attention for the application in electronic and optoelectronic devices. Contacts, which are the communication links between these 2D materials and external circuitry, have significant effects on the performance of electronic and optoelectronic devices. However, the performance of devices based on 2D semiconductors (SCs) is often limited by the contacts. Here, we provide a comprehensive overview of the basic physics and role of contacts in 2D SCs, elucidating Schottky barrier nature and Fermi level pinning effect at metal/2D SCs contact interface. The progress of contact engineering, including traditional metals contacts and metallic 2D materials contacts, for improving the performance of 2D SCs based devices is presented. Traditional metal contacts, named 3D top and edge contacts, are discussed briefly. Meanwhile, methods of building 2D materials contacts (2D top contact and 2D edge contact) are discussed in detail, such as chemical vapor deposition (CVD) growth of 2D metallic material contacts, phase engineered metallic phase contacts and intercalation induced metallic state contacts. Finally, the challenges and opportunities of contact engineering for 2D SCs are outlined.