QCD is believed to have various phase transitions at nonzero density and temperature. In this talk, I will discuss two topics related to their experimental searches in relativistic heavy-ion collisions. The first topic is concerned with a search for the QCD critical point using fluctuation observables. I will overview recent theoretical and experimental progress in this field especially focusing on the non-Gaussian fluctuations of conserved charges. I will then discuss a more ambitious subject to search for color superconductivity. Near the phase boundary of color superconducting phases, diquark fluctuations are enhanced as the soft mode of the phase transition. We show that these fluctuations cause an anomalous enhancement of the dilepton production rate at low invariant-mass region through the analysis of the photon self-energy including diquark fluctuations. We argue that this enhancement can be used for an experimental signal of the precursor of color superconductivity.