  We present an overview of recent nonperturbative results in the theory of
heat kernel and its late time asymptotics responsible for the infrared behavior
of quantum effective action for massless theories. In particular, we derive the
generalization of the Coleman-Weinberg potential to physical situations when
the field is not homogeneous throughout the whole spacetime. This
generalization represents a new nonlocal and nonperturbative action accounting
for the effects of a transition domain between the spacetime interior and its
infinity. In four dimensions these effects delocalize the logarithmic
Coleman-Weinberg potential, while in $d>4$ they are dominated by new powerlike
and renormalization-independent nonlocal structure. Nonperturbative behavior of
the heat kernel is also constructed in curved spacetime with
asymptotically-flat geometry, and its conformal properties are analyzed for
conformally invariant scalar field. The problem of disentangling the local
cosmological term from nonlocal effective action is discussed.
