Phase transition from hadronic matter to quark-gluon matter is discussed for various regimes of temperature and baryon number density. For small and medium densities, the phase transition is accurately described in the framework of the Field Correlation Method, whereas at high density predictions are less certain and leave room for the phenomenological models. We study formation of multiquark states (MQS) at zero temperature and high density. Relevant MQS components of the nuclear matter can be described using a previously developed formalism of the quark compound bags (QCB).Partial-wave analysis of nucleon-nucleon scattering indicates the existence of 6QS which manifest themselves as poles of P -matrix. In the framework of the QCB model, we formulate a selfconsistent system of coupled equations for the nucleon and 6QS propagators in nuclear matter and the G-matrix. The approach provides a link between high-density nuclear matter with the MQS components and the cumulative effect observed in reactions on the nuclei, which requires the admixture of MQS in the wave functions of nuclei kinematically.6QS determine the natural scale of the density for a possible phase transition into the MQS phase of nuclear matter. Such a phase transition can lead to dynamic instability of newly born protoneutron stars and dramatically affect the dynamics of supernovae. Numerical simulations show that the phase transition may be a good remedy for the triggering supernova explosions in the spherically symmetric supernova models. A specific signature of the phase transition is an additional neutrino peak in the neutrino light curve. For a Galactic core-collapse supernova, such a peak could be resolved by the present neutrino detectors. The possibility of extracting the parameters of the phase of transition from observation of the neutrino signal is discussed also.