Formic acid is a liquid organic hydrogen carrier giving hydrogen on demand using catalysts. Metal complexes are known to be used as efficient catalysts for the hydrogen production from formic acid decomposition. Their performance could be better than those of supported catalysts with metal nanoparticles. However, difficulties to separate metal complexes from the reaction mixture limit their industrial applications. This problem can be resolved by supporting metal complexes on the surface of different supports, which may additionally provide some surface sites for the formic acid activation. The review analyzes the literature on the application of supported metal complexes in the hydrogen production from formic acid. It shows that the catalytic activity of some stable Ru and Ir supported metal complexes may exceed the activity of homogeneous metal complexes used for deposition. Non-noble metal-based complexes containing Fe demonstrated sufficiently high performance in the reaction; however, they can be poisoned by water present in formic acid. The proposed review could be useful for development of novel catalysts for the hydrogen production.