The exact mechanisms responsible for heating the solar atmosphere in regions such as the chromosphere (partially ionized) and the corona (fully ionized) remain quantitatively unknown. This thesis demonstrates that the ions can be heated by Alfven waves with low frequencies in fully and partially ionized low beta plasmas, which is contrary to the customary expectation. For the partially ionized case, we find the heating process to be less efficient than the scenario with no ion-neutral collisions, and that the heating efficiency depends on the ratio of ion-neutral collision frequency to the ion gyrofrequency. For Alfven waves propagating obliquely to the background magnetic field in fully ionized plasmas, we find the heating process to be more efficient than the situation with Alfven waves propagating along the background magnetic field. Furthermore, the simulation results show the parallel kinetic temperature can become even larger than the perpendicular component for the case of obliquely propagating Alfven waves.