Since 1970 surface brightness profiles of disc galaxies were classified as Type-I, single falling exponentials, or Type-II, broken exponentials with steeper decline in the outskirts. For the past decade Type-III profiles, (antitruncations), with a shallower fall-off in the outskirts, have been shown to occur in a significant fraction of galaxy discs. Here we give a brief overview, characterizing these profiles and their distribution with galaxy type, with a look at recent explanations of their causes, and how they fit into the picture of galaxy evolution.