Counting the number of degrees of freedom for capillary systems is often not simple because of complications with the mechanical equilibrium constraints associated with curved liquid-fluid interfaces and curved three-phase contact lines. In this paper, the inapplicability of the Gibbs phase rule to capillary systems containing curved interfaces is discussed. For a general capillary system, the presence of curved interfaces results in fewer mechanical equilibrium constraints and hence more degrees of freedom, in comparison with composite bulk phase systems. A recently derived phase rule for moderately curved capillary systems is reviewed in this paper. Some experimental confirmation of the number of degrees of freedom predicted by such a phase rule is discussed. Furthermore, by counting properly the total number of variables required to describe the equilibrium state and the total number of equilibrium constraints, a phase rule for capillary systems containing highly curved surfaces and three-phase lines is derived. The comparisons show that there is not only a difference between the phase rule for capillary systems, but also a difference between the phase rule for moderately curved capillary systems and the phase rule for highly curved capillary systems. Such differences in the number of degrees of freedom result from the curvature effects of the interfaces.