Scottish botanist and geographer from Campster, Caithness who was educated at the Universities of Edinburgh, Leyden, Copenhagen, and Rostock. He was appointed botanist to the British Columbia Expedition (1863-1866) and led the exploration of Vancouver Island (1864). On this journey he was accompanied by artist and climber Edward Whymper who later became a collector of plants with Brown in Greenland. Brown made a study of the glaciation of Greenland and collected fossil plants, now at the Department of Palaeontology of The Natural History Museum. He was subsequently appointed Lecturer in Natural History at Heriot-Watt College, Edinburgh (1869-1876). In 1876 he moved to London and wrote for a number of popular science publications. To distinguish him from several other botanists named Robert Brown, his home town of Campster is sometimes appended to his name. Lecidea campsteriana Linds. is named in his honour through this association.