  We outline a theoretical approach supporting strong phase transitions from
normal nuclear matter to the deconfined quark-gluon plasma, in the equation of
state (EOS) for compact star matter. Implications of this hypothesis are
discussed for astrophysical applications. Special emphasis is devoted to
potentially detectable signatures, which can be directly related with the
occurrence of a sufficiently strong phase transition. Therefore, simulations of
core-collapse supernovae and binary compact star mergers are considered,
including the subsequent emission of gravitational waves and, in the case of
supernova, in addition the neutrinos play the role of messengers.
