The Crosier Brothers and Fathers became missionaries to the Asmat in 1958, a few years after the Asmat invited the first missionaries to come to their land. Starting with the first four men, the Crosiers worked alongside the Asmat to preserve and develop their dignity, environment, artistic and spiritual heritage and dreams of a better life.

Since the beginning of the mission, the Crosiers have collected Asmat carvings and artifacts: a challenging task in a jungle where heat and humidity quickly destroy wooden and fibrous objects.

Under the leadership of Bishop Alphonse Sowada, osc, first bishop of Agats-Asmat, the Crosiers opened the Asmat Museum of Culture and Progress in Agats in 1973. In 1975, they established the Crosier Asmat Museum in Hastings, Nebraska. In 1995, the American Museum of Asmat Art was officially established in St. Paul, Minnesota. 

In 2007, the Museum became part of the University of St. Thomas in St. Paul, Minnesota, with a continuing commitment to fulfilling the Museum's mission. Long-term plans include a permanent gallery on the university campus, integration of the collection into university art history programs, K-12 educational outreach efforts, and continued collaborative off-campus exhibitions. The Museum will be renamed "The American Museum of Asmat Art at the University of St. Thomas."