Despite great advances in observations and modelling, the problem of solar and stellar heating still remains one of the most challenging problems of space physics. To find a definite answer to what sort of mechanisms act to heat the plasma to a few million degrees requires a collaborative effort of small scales observations, large capacity numerical modelling and complicated theoretical approaches. A unique theory should incorporate aspects such as the generation of energy, its transport and dissipation. Up to now, the first two problems are rather clarified. However, the modality of transfer of magnetic or kinetic energy into heat is a question still awaiting for an answer. In the present paper we review the various popular heating mechanisms put forward in the existing extensive literature. The heating processes are, somewhat arbitrarily, classified as hydrodynamic, magnetohydrodynamic or kinetic based on the characteristics of the model medium. These mechanisms are further divided based on the time scales of the ultimate dissipation involved (i.e. AC and DC heating, turbulent heating). In particular, special attention is paid to discuss shock dissipation, mode coupling, resonant absorption, phase mixing, and, reconnection. Finally, we briefly review the various heating mechanisms proposed to heat other stars.