The son of a Lutheran minister interested in natural history, Runguis began to draw the animal world at an early age. In 1889 he enrolled in the Berlin Art School, and entered the Berlin Academy of Fine Arts, and the Berlin School of Applied Arts the following year. Among his teachers were Max Koch and Paul Meierheim, a noted wildlife painter. Runguis spent 1891 in the Prussian cavalry, where he developed his skills as a marksman.
Runguis first visited the United States in 1894, joining an uncle on a hunting expedition in Maine. He also spent time in Wyoming before briefly returning to Germany in 1896. At some time in the 1890s he was studying with Charles Noel Flagg in Hartford, Connecticut, but by 1897, he was settled in Brooklyn, New York, and was doing illustrations for sports periodicals, while trying to establish himself as a painter. He made frequent trips to Wyoming, and to New Brunswick, Maine, in the turn-of-the-century years; 1904 was passed in the Yukon with the naturalist, Charles G. Sheldon. In the year following this extensive trip, Rungius became a United States citizen.
In 1910 he acquired a studio in Manhattan, which led to his widening acquaintance in the New York art world, and visited the Canadian Rockies for the first time. Thereafter he used his summers to gather material for his paintings of animals in the wild in Wyoming, or in Alberta, Canada. As Wyoming became more settled, he increasingly sought his favored subject matter further north, finally building a studio in Banff in 1921, which he visited annually to the year before his death. Prior to 1914, when he devoted himself completely to painting, he was an avid hunter, and a companion to Theodore Roosevelt on several hunting expeditions. From 1912 to 1936, Rungius was much occupied in painting the collection of the New York Zoological Society.
Rungius's reputation was based on his portrayal of big game animals of the American West in their natural surroundings, yet around 1912, he began to give primary attention to landscape, alone, as the subject of his paintings. By the mid-1920s he had returned to his, and his public's first love, the caribou, antelop, bighorn sheep, and bear of the Canadian Rockies.
Rungius was active in many arts organizations including the Society of Animal Painters and Sculptors, the Painters of the Far West, and the National Arts Club. He was also a charter member of the Camp Fire Club of America, and an honorary member of the Boy Scouts of America. Rungius served one three-year term on the Academy's Council, 1927-30. For contributions to Academy annual exhibitions he received a Speyer Memorial prize in 1925, a Carnegie prize in 1926, and a Saltus Medal in 1929. In the early 1950s his studio in Banff, Canada, was made into a museum.
