The recent realization of topology as a mathematical concept in condensed matter systems has shattered Landau's widely accepted classification of phases by spontaneous symmetry breaking as he famously said, "a particular symmetry property exists or does not exist." Topological materials (TMs) such as topological insulators and topological semimetals, are characterized by properties that depend on the topology of the band structure. Such dependence has drastic implications on the optical, electrical, and thermal properties of the material. Fundamental physics of TMs is currently under active research in condensed matter, materials science, and high energy physics. In this review, recent advances in exploiting the unique properties of TMs to realize functional optoelectronic devices are surveyed. Current and future applications that are, or may be, enabled by their unique properties are discussed. Although many theoretical ideas have been proposed over the past decade or so on using TMs in optoelectronic applications, the focus will be on experimentally realized devices.