Formic acid and formates are often produced by hydrogenation of CO2 with hydrogen over homogeneous catalysts. The present review reports recent achievements in utilization of heterogeneous catalysts. It shows that highly dispersed supported metal catalysts are able to carry out this reaction by providing activation of hydrogen on the metal sites and activation of CO2 or bicarbonate on the support sites. Important advances have recently been achieved through utilization of catalysts using CxNy materials as supports. The high activity of these catalysts could be assigned to their ability to stabilize the active metal in a state of single-metal atoms or heterogenized metal complexes, which may demonstrate a higher activity than metal atoms on the surface of metal nanoparticles.