The problem of many interacting fermions touches many areas of physics, from superconductivity to dense nuclear matter.  One of the richest fermionic systems is a dilute gas of fermionic alkali atoms in the regime where the atom-atom interactions grow very strong.  This is the so-called BCS-BEC crossover problem.  This colloquium will give an overview of that problem, including a discussion of some insights that can be gleaned by studying the strongly-coupled 2-, 3-, and 4-body subsystems.