  We briefly review some current theoretical and experimental aspects of the
problem of a single spinless impurity in a 3D polarised atomic Fermi gas at
zero temperature where the interactions can be tuned using a wide Feshbach
resonance. We show that various few-body states in vacuum composed of the
impurity and background gas atoms (single impurity, dimer, trimer, tetramer)
give rise to corresponding dressed states ({\em polaron}, {\em dimeron}, {\em
trimeron}, {\em tetrameron}) in the gas and inherit many of their
characteristics. We study the ground state focussing on the choice of wave
function and its properties. We raise a few unsolved problems: whether the
polaron and dimeron are really separate branches, what other few-body states
might exist, the nature of the groundstate for large numbers of particle-hole
pairs and why is the polaron ansatz so good. We then turn to the excited
states, and to the calculation of the effective mass. We examine the bounds on
the effective mass and raise a conjecture about that of composite quasiparticle
states.
