The Fermi-Hubbard model is a cornerstone of modern condensed matter theory. It describes interacting electrons in solids, notably featuring a metal to Mott insulator transition. In its extended SU(N>2)-symmetric form, it has already attracted much interest in the context of multi-orbital materials such as transition-metal oxides. In addition, it has been predicted to exhibit novel quantum magnetic phases and spin liquids with topological order. In this talk, I will give a general introduction to the SU(N) Fermi-Hubbard model and, after discussing its general features, I will present its experimental realization with ultracold alkaline-earth atoms in optical lattices. To this aim, I will first describe in detail how SU(N)-symmetry emerges for fermionic atoms with alkaline-earth-like electronic structure. Owing to the existence of metastable excited states as well as to the strong decoupling between the nuclear and the electronic angular momenta, these atoms are particularly well suited for the investigation of SU(N) symmetric models with orbital degrees of freedom. I will then present some experimental results obtained using ultracold ytterbium atoms trapped in a three-dimensional optical lattice. In particular, I will report on the study of the equation of state of such system in various interaction regimes and for distinct values of N, directly showing the emergence of an SU(N)-symmetric incompressible Mott insulating phase. I will finally discuss perspectives towards probing novel SU(N) magnetic phases in optical lattices.