There are at least two classes of problems where interfaces contribute to an instability. In the first class, two immiscible phases are separated by an interface. The problems of this class are flow problems; one fluid displaces the other and a typical example is that of the instability of jets. The curvature of the interface determines local pressure variations and these translate into flows, sometimes reinforcing a displacement. The base state is an equilibrium state and cylindrical geometries give the interface two roles to play. There are two competing curvature effects: the stabilizing axial variations of the surface are accompanied by destabilizing diameter variations, viz., the diameter at a crest exceeds the diameter at a trough. These two effects alone are enough to determine the critical point of a jet. This arises from Rayleigh's work principle. The second class of problems are phase change problems, viz., material crosses the interface and solidification and electrodeposition are representative examples. These are diffusion problems. Curves of growth constants versus disturbance wave numbers are a classical way to study the physics of most instability problems. We will show how and why these two classes of problems have widely different signatures on the growth curves.