The theory of totally disconnected locally compact (t.d.l.c.)~groups has advanced considerably in recent years. Lie groups over the valued fields ?_p of p-adic numbers and ?_q((X)) of formal Laurent series over the finite field ?_q are t.d.l.c.~groups, and the Lie theory of these groups is an important source of inspiration for the more general theory. Other classes of t.d.l.c.~groups include all profinite groups, the isometry groups of locally finite graphs and the completions of Kac-Moody groups over finite fields. The question of how close the classes of known examples come to exhausting all t.d.l.c.~groups has still to be resolved. This talk will survey the principal themes of research on t.d.l.c.~groups and indicate how they relate to the Lie group case.