Thermoelectric materials can be used for solid state power generation and heating/cooling applications. The figure of merit of thermoelectric materials, ZT, which determines their efficiency in a thermoelectric device, remains low for most conventional bulk materials. Nanoscale and nanostructured thermoelectric materials are promising for increasing ZT relative to the bulk. This review introduces the theory behind thermoelectric materials and details the predicted and demonstrated enhancements of ZT in nanoscale and nanostructured thermoelectric materials. We discuss thin films and superlattices, nanowires and nanotubes, and nanocomposites, providing a ZT comparison among various families of nanocomposite materials. We provide some perspectives regarding the origin of enhanced ZT in nanoscale and nanostructured materials and suggest some promising and fruitful research directions for achieving high ZT materials for practical applications.