The experimental realization of stable, ultracold Fermi gases near a Feshbach resonance allows to study gases with attractive interactions of essentially arbitrary strength. They extend the classic paradigm of BCS into a regime which has never been accessible before. We review the theoretical concepts which have been developed in this context, including the Tan relations and the notion of fixed points at zero density, which are at the origin of universality. We discuss in detail the universal thermodynamics of the unitary Fermi gas which allows a fit free comparison between theory and experiment for this strongly interacting system. In addition, we address the consequences of scale invariance at infinite scattering length and the subtle violation of scale invariance in two dimensions. Finally we discuss the fermionic excitation spectrum accessible in momentum-resolved RF-spectroscopy and the origin of universal lower bounds for the shear viscosity and the spin diffusion constant.