Starting with the fundamental and general criterion for a spontaneous process in thermodynamics, delta S[subscript tot] greater than or equal to 0, we review its relationships to other criteria, such as delta A and delta G, that have limitations. The details of these limitations, which can be easily overlooked, are carefully explicated. We also bring in the important example of electrical energy to show how criteria for spontaneity are properly applied to electrochemical cells. The analysis in this article gains clarity from use of the "global" formulation of thermodynamics and from carrying out finite changes of thermodynamic properties rather than manipulating differential changes. Several examples are given. (Contains 2 tables.)