Heat is an abundant
but often wasted source of energy. Thus, harvesting
just a portion of this tremendous amount of energy holds significant
promise for a more sustainable society. While traditional solid-state
inorganic semiconductors have dominated the research stage on thermal-to-electrical
energy conversion, carbon-based semiconductors have recently attracted
a great deal of attention as potential thermoelectric materials for
low-temperature energy harvesting, primarily driven by the high abundance
of their atomic elements, ease of processing/manufacturing, and intrinsically
low thermal conductivity. This quest for new materials has resulted
in the discovery of several new kinds of thermoelectric materials
and concepts capable of converting a heat flux into an electrical
current by means of various types of particles transporting the electric
charge: (i) electrons, (ii) ions, and (iii) redox molecules. This
has contributed to expanding the applications envisaged for thermoelectric
materials far beyond simple conversion of heat into electricity. This
is the motivation behind this review. This work is divided in three
sections. In the first section, we present the basic principle of
the thermoelectric effects when the particles transporting the electric
charge are electrons, ions, and redox molecules and describe the conceptual differences
between the three thermodiffusion phenomena. In the second section,
we review the efforts made on developing devices exploiting these
three effects and give a thorough understanding of what limits their
performance. In the third section, we review the state-of-the-art
thermoelectric materials investigated so far and provide a comprehensive
understanding of what limits charge and energy transport in each of
these classes of materials.