  We give a short introduction to the subject of representation growth and
representation zeta functions of groups, omitting all proofs. Our focus is on
results which are relevant to the study of arithmetic groups in semisimple
algebraic groups, such as the special linear group of degree n over the ring of
integers. In the last two sections we state several results which were recently
obtained in joint work with N. Avni, U. Onn and C. Voll.
