In the context of reviewing noncompact lattice gauge models at zero an
d finite temperatures, we study in detail the contribution of the inva
riant measure and of the timelike plaquette configurations to correlat
ion functions, analyze the problem of the compactness of potentials wi
th respect to confinement, and indicate features that are important in
dealing with Wilson gauge theory in the weak-coupling region. A metho
d for constructing an effective confining noncompact model is also pro
posed.