Kinetic plasma physics of the solar corona and solar wind is reviewed with emphasis on the theoretical understanding of in situ measurements of solar wind particles and waves, as well as on remote-sensing observations of the solar corona made by means of ultraviolet spectroscopy and imaging. In order to explain coronal and solar wind heating, the microphysics of non-thermal distribution functions and the dissipation of various forms of mechanical, electric and magnetic energy at small scales (e.g., contained in plasma waves, turbulences or non-uniform flows) is addressed. We inspect the basic assumptions underlying the classical transport theory and the related collisional heating rates, and also describe alternatives associated with wave-particle interactions. We elucidate the kinetic aspects of heating the solar corona and interplanetary plasma through Landau- and cyclotron-resonant damping of plasma waves, and analyze in detail wave absorption and micro instabilities. Important aspects associated with the virtues and limitations of fluid models, either single- and multi-species or magnetohydrodynamic and multi-moment models as well as kinetic models, for coronal heating and solar wind acceleration are discussed. Promising areas and perspectives for future research are outlined.