Recent progress in studies on quantum chromodynamics (QCD) phase transition and related critical phenomena within the functional renormalization group (fRG) approach were reviewed, including the nonperturbative critical exponents and baryon number fluctuations, which are pertinent to the critical end point (CEP) in the QCD phase diagram. The fRG is a nonperturbative continuum field approach, in which quantum thermal fluctuations are successively integrated with the evolution of the renormalization group (RG) scale. Different methods of finding solutions to the flow or fixed-point equations of a nonperturbative effective potential have been discussed, for example, the Taylor expansion, expansion of the spatial dimension ε=4-d, and the recently proposed direct solution of the global potential. Furthermore, the baryon number of fluctuations is relevant to the critical phenomena of the CEP. Both have been discussed, and one explores the underlying reasons for the observed non-monotonic dependence of the kurtosis of the net proton number of distributions on collision energy in experiments.