  In these notes I provide an overview of ongoing theoretical and experimental
research on ultracold atomic mixtures composed by 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 ($^6$Li) and
chromium ($^{53}$Cr) atoms, currently investigated in our lab, highlighting its
peculiar properties with respect to other Fermi mixtures nowadays available.
Finally, I summarize recent experimental progress achieved in producing and
characterizing this novel system, providing an outlook for future studies based
on ultracold $^6$Li-$^{53}$Cr Fermi mixtures.
