  The transition to quark matter can take place in neutron stars. The structure
of a hybrid star, containing a core made of quark matter is discussed. The
maximum mass of the non-rotating hybrid star turns out to be 1.6 M_s. Possible
signatures of the quark phase as pulsar's timing, cooling rate etc. are briefly
analyzed. The deconfinement transition can also take place during the
pre-supernova collapse. This possibility is studied by introducing a finite
temperature EOS. The dependence of the latter on the proton fraction is shown
to be crucial. The softening of the EOS at densities just above nuclear matter
saturation density for Z/A = 0.3 helps in obtaining an explosion. At the same
time, at larger densities the EOS is stiff enough to support a neutron star
compatible with observations.
