Thermoelectric generators (TEGs) can directly convert waste heat into electrical power. In the last few decades, most research on thermoelectrics has focused on inorganic bulk thermoelectric materials and corresponding devices, and their thermoelectric properties have been significantly improved. An emerging topic is flexible devices, where the use of bulk inorganic materials is precluded by their inherent rigidity. The purpose of this paper is to review the research progress on flexible thermoelectric materials and generators, including theoretical principles for TEGs, conducting polymer TE materials, nanocomposites comprised of inorganic nanostructures in polymer matrices and fully inorganic flexible TE materials in nanostructured thin films. Approaches for flexible TEGs and components are reviewed, and remaining challenges discussed. (C) 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).