Power law distributions are routinely used to describe the particle spectra obtained in the high energy collision events (like proton-proton collisions). The phenomenological Tsallis distribution is one such example which has wide application in many other branches of Physics. We shall discuss the different formulations of the Tsallis statistical mechanics and the transverse momentum spectra calculable from those formulations. Afterward, we shall establish the connection between the exact Tsallis spectra and the phenomenological forms used in the literature.