The Museum, founded in 2004, occupies about four hundred square metres of the former Damiano Chiesa Elementary School in the Servola area of Trieste. The Museum was created on the initiative of the Associazione Triestina Amici del Presepio to exhibit contemporary cribs.

Over time, hundreds of Nativity scenes have been added to the original works, some acquired and others donated by authors or private collectors. Active collaboration by the city council enabled the exhibition to become a museum.

The Museo del Presepio holds about 500 works that testify to Trieste's tradition, creativity, art and culture, and offer a broad and comprehensive overview of the various interpretations and presentations of the Nativity in Italy and the world.

A vast range of materials has been used in their construction, including paper, wood, wax, polystyrene, shells, cigarette filters, cardboard, cork and terracotta. There are spectacular nativity scenes, dioramas, reproductions of paintings, artistic works and a section reserved for the so-called "Triestini" cribs, set in scenes that reproduce characteristic views of the city and its province.

The Museum can provide access, on request, to a crib-themed library and a collection of DVDs on exhibitions, courses on crib techniques, and crib history. The Museum organises conferences on the crib, and courses in crib technique are presented annually in October.