The incompiuta or "unfinished" church of Venosa is part of the city's archaeological park, where the complex of the Abbey of the Most Holy Trinity was built in the 8th century. Some 300 years later, the "Old Church," as the abbey was known, was no longer sufficient to host the growing number of faithful, and so the construction of a new structure began at the end of the 11th century.

The plan was to expand the old church building with a vast extension behind the apse, designed with Roman, Lombard, and Norman architectural influences. Yet the construction proceeded slowly, probably because of the poor finances of the Benedectine monks that were subsidizing the project. Then the project hit another snag. The monastic order was abolished in 1297 by Pope Boniface VIII and the complex was given to the Knights Hospitaller the same year, who decided not to complete the construction of the new church, leaving it in ruins.

Over the years, some additions to the deserted church were implemented, such as a portal in the 14th century and a bell tower in the 16th century. But the main building is still unfinished today, almost a thousand years after its construction began.