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Since the very first detection of gravitational waves from a binary neutron star merger, in August 2017, the field of relativistic computational astrophysics has gained increasing attention. However, theoretical studies of compact stars, such as (proto)neutron stars, core-collapse supernovae, and binary neutron star mergers, have to deal with one caveat, namely, the yet incompletely known equation of state. In particular at high baryon density. The equation of state defines not only bulk properties of matter, such as pressure, energy density, and entropy but also transport properties, relevant for the treatment of neutrino. It is therefore of fundamental interest to define global parameters of compact stars, which can be related via empirical relations being independent of the equation of state. These are known as universal relations. In this talk, I will revisit the concept of universality in the context of rapidly and non-rotating neutron stars. Particular interest will be devoted to systems that feature a hadron-quark matter phase transition. I will further report on recent results of astroseismology related to the mode analysis of core-collapse supernovae simulations. These modes are excited due to various phenomena, e.g., radial oscillations of the central protoneutron star and the propagation of pressure waves, which indicate the presence of a possible universality too.