Well-known compact astrophysical objects comprise white dwarfs, neutron stars and black holes. In contrast, boson stars represent hypothetical compact objects, that have been invoked for a variety of objects, ranging from dark matter via black hole impostures to galactic halos. Properties, stability, and astrophysical viability of these solutions will be studied further. Neutron stars, on the other hand, are well established objects, whose properties depend sensitively on the equation of state of the baryonic matter. However, recently it was shown that when properly scaled, some of their properties become (almost) independent of the equation of state. The extension of these studies to generalized models of gravity has been started and should yield valuable information for the comparison with astrophysical data.