Support effects in heterogeneous catalysis are evolving as an important field of investigation to optimize catalyst properties. The cobalt-based Fischer-Tropsch (FT) catalysts usually consist of metallic cobalt nano-crystallites dispersed on a support material. The present review surveys the progress that has been made over the last couple of decades in the area of the effect of the support and its surface modifications in cobalt-based FT synthesis. Different catalyst supports such as alumina, silica, titania, niobia, zirconia, zeolite, ceria, carbon-based materials, silicon carbide, aluminum phosphate, hydrotalcite, metal-organic frameworks, and metal foams are discussed and compared with classical supports like alumina or silica wherever permitted. Properties such as metal-support interactions, the support-induced size and morphology of the cobalt nanocrystallites (textural properties of the support), changes in the electronic properties of the cobalt clusters, and the acid/base nature of the support are examined, and wherever possible the activity and/or selectivity in FT synthesis is discussed. This review also summarizes findings on new and promising supports for FT catalysts. Guidance for support modifications and choice of the support as functions of the product selectivity in the FT process is also proposed.