  We discuss different exotic phases and components of matter from the crust to
the core of neutron stars based on theoretical models for equations of state
relevant to core collapse supernova simulations and neutron star merger.
Parameters of the models are constrained from laboratory experiments. It is
observed that equations of state involving strangeness degrees of freedom such
as hyperons and Bose-Einstein condensates are compatible with 2M$_{solar}$
neutron stars. The role of hyperons is explored on the evolution and stability
of the protoneutron star (PNS) in the context of SN1987A. Moment of inertia,
mass and radius which are direct probes of neutron star interior are computed
and their observational consequences are discussed. We continue our study on
the dense matter under strong magnetic fields and its application to
magnetoelastic oscillations of neutron stars.

High Energy Astrophysical Phenomena