The origin of cosmic rays (CR) is supposed to be closely connected with supernovae (SNe) which create the conditions favorable for various mechanisms of the CR acceleration to operate effectively. First, modern ideas about the physics of the SN explosion are briefly discussed: the explosive thermonuclear burning in degenerate white dwarfs resulting in Type Ia SNe and the gravitational collapse of stellar cores giving rise to other types of SNe (Ib, Ic, IIL, IIP). Next, we survey some global properties of the SNe of different types: the total explosion energy distribution of various components (kinetic energy of the hydrodynamic flow, electromagnetic radiation, temporal behavior of the neutrino emission and individual energies of different neutrino flavors). Then, we discuss in the possibility of direct hydrodynamic acceleration by the shock wave breakout and the properties of the SN shocks in the circumstellar medium. Then the properties of the neutrino radiation from the core-collapse SNe and a possibility to incorporate both the LSD Mont Blanc neutrino event and that recorded by the K II and IMB detectors into a single scenario are described in detail. Finally, the issues of the neutrino nucleosynthesis and of the connection between supernova and gamma-ray bursts are discussed.