The topic of the present lecture notes are two-species quantum mixtures composed of a deeply degenerate Fermi gas and a second component, the latter being fermionic or bosonic. A key ingredient is the possibility to tune the s-wave interaction between the different species by means of magnetically controlled Feshbach resonances, which allow us to investigate regimes of strong interactions. In two case studies, we review our experiments on mixtures of ⁶Li fermions with fermionic ⁴⁰K or bosonic ⁴¹K atoms and on mixtures of fermionic ¹⁶¹Dy with ⁴⁰K atoms. We cover various topics of fermionic quantum many-body physics, ranging from impurity physics and quasiparticles over phase separation to the formation of ultracold molecules and progress towards novel superfluids.