  The interior of compact stars is usually divided into two major parts, the
outer part called crust and the inner part called core. There are several
possibilities for the composition of these parts. One is a hybrid star, in
which the crust contains nuclear matter, while the inner core contains quark
matter. Since at large baryon densities one can work with effective models, and
nuclear and quark matter are usually described by different models, some
unification of the two parts is needed. We show two different approaches for a
composite model and some recent developments in hybrid star constructions using
the extended linear sigma model for modeling the quark matter at the core.
