Mixed-component metal-organic frameworks (MC-MOFs) are metal-organic frameworks that have different linkers or metals with the same structural role. Many of these mixed-ligand or mixed-metal MOFs are solid solutions, in which the proportions of the ligands or metals can be adjusted or even controlled. These MC-MOFs can be prepared directly, using more than one metal or ligand in the synthesis, or formed by post-synthetic modification. A second class of MC-MOFs have core-shell structures, and these can be prepared through epitaxial growth of one MOF on the surface of another or post-synthetic modification of the crystal surfaces. This review describes the syntheses, structures and properties of mixed-ligand, mixed-metal and core-shell MOFs, and highlights some of the potential benefits in functionality that these materials have.