The heating of the solar corona is thought to occur through the dissipation of magnetohydrodynamic (MHD) wave energy and/or through energy released during the reconnection of magnetic fields. Observations of emission line fluxes and widths provide constraints that must be satisfied by the proposed heating and dissipation processes. Although observations of the Sun provide the most detailed information, observations of other main-sequence stars lead to trends in coronal parameters with simple indicators of stellar magnetic activity that must also be explained by any successful theory. Observations of the quiet (average) solar transition region and inner corona are broadly consistent with coronal heating by high frequency Alfvén waves, which might be generated by magnetic reconnection.