Ongoing and upcoming integral-field spectroscopic surveys will provide stellar kinematic maps of thousands of nearby galaxies across the Hubble sequence. For the first time, we have been able to construct Schwarzschild dynamical models that fit in detail elliptical through spiral galaxies from the CALIFA survey in a homogeneous way. This orbit superposition method allows us to uncover the luminous and dark matter in galaxies without (astro)physically unjustified assumptions on shape and velocity anisotropy made in common dynamical approaches. Moreover, the inferred intrinsic orbital structure enables us to dynamically decompose galaxies into different components such as bulges, thin and thick disks. Subsequently, we can for each component robustly derive its mass distribution as well as internal rotation, velocity dispersion and higher-order dynamics. In this way, we obtain a detailed physical insight into nearby galaxies from statistically well-defined samples, which in turn provides a true benchmark for galaxy formation models in a cosmological context.