Crystalline silicon (c-Si) is the dominating photovoltaic technology today, with a global market share of about 90%. Therefore, it is crucial for further improving the performance of c-Si solar cells and reducing their cost. Since 2014, continuous breakthroughs have been achieved in the conversion efficiencies of c-Si solar cells, with a current record of 26.6%. The great efficiency boosts originate not only from the materials, including Si wafers, emitters, passivation layers, and other functional thin films, but also from novel device structures and an understanding of the physics of solar cells. Among these achievements, the carrier-selective passivation contacts are undoubtedly crucial. Current carrier-selective passivation contacts can be realized either by silicon-based thin films or by elemental and/or compound thin films with extreme work functions. The current research and development status, as well as the future trends of these passivation contact materials, structures, and corresponding high-efficiency c-Si solar cells will be summarized.