Madsen is known for her works in installation, sculpture, photography, and video. Her vast collections of cast-off 20th-century industrial matter--spark plugs, machine parts, welding masks, light switches, rubber, plastic, prosthetics, artificial eyes, and much more–serve as fodder for her work depicting a voracious world gone awry.
Madsen's recent videos have been broadcast in Germany, France, and Italy. She has had solo exhibitions in Italy, Scotland, the Czech Republic, Serbia, and the United States. Her works have been shown in numerous international exhibitions in Europe, Asia, and the Middle East. Her art has been exhibited at the New York Public Library, the Corcoran Gallery of Art in Washington, D.C., Pratt Institute, Brooklyn, the Lowry Lab Theater in Minneapolis, and at the International Print Center New York. She has been a visiting artist in New Zealand, Serbia, Belgium, Scotland, the Czech Republic, and Singapore. Her works are in the collections of the New York Public Library, Library of Congress, Dartmouth College, University of Sharijah: United Arab Emirates, Guanlan Art Center; Shenzhen, China, and Amoco Corporation.