  After a brief review of the theory of cosmological perturbations, I highlight
some recent progress in the area of reheating in inflationary cosmology,
focusing in particular on parametric amplification of super-Hubble cosmological
fluctuations, and on the role of noise in the resonance dynamics (yielding a
new proof of Anderson localization). I then discuss several important
conceptual problems for the current realizations of inflation based on
fundamental scalar matter fields, and review some new approaches at solving
these problems.
