The conceptual and mathematical difficulties associated with contact angle equilibrium are reviewed and analyzed. The main discussion is centered around the theory of the intrinsic contact angle and its dependence on the three-phase mutual interactions in the vicinity of the contact line. Rigorous thermodynamic derivation of the equilibrium condition is presented, emphasizing the question of the correct presentation of the colloidal interactions near the contact line. This is followed by the presentation of various case studies, in order of increasing complexity. The line tension concept is also discussed, and its implications are compared with those of the general thermodynamic treatment.