Some recent developments have been made in the study of phase transitions in grand unified theories (GUTs) in which radiatively induced corrections to the effective potential play an important role (e. g. Coleman-Weinberg models). The course of the phase transition is shown to depend sensitively on the choice of parameters of the theory. A restricted class of parameters, excluding the simplest SU(5) GUT model, is found to lead to an inflationary Universe. An heuristic argument is given to show that the spectrum of fluctuations in such models (on observable scales) is scale invariant and a dimensional argument is proposed to explain the amplitude of the resultant fluctuations. Only a much more restricted class of GUT models is found to yield an inflationary Universe with fluctuations that are not so big as to be inconsistent with the isotropy and homogeneity in the observable Universe.