In these notes I provide an overview of ongoing theoretical and experimental research on ultracold atomic mixtures composed of two different fermionic species. First, I describe a general and simple framework that should allow also a non-expert reader to understand the rich few-body phenomena connected with such systems, and their possible impact at the many-body level. I then move to discuss the specific combination of fermionic lithium (⁶Li) and chromium (⁵³Cr) atoms, currently investigated in our lab, highlighting its peculiar properties with respect to other Fermi mixtures available nowadays. Finally, I summarize recent experimental progress achieved in producing and characterizing this novel system, providing an outlook for future studies based on ultracold ⁶Li-⁵³Cr Fermi mixtures.