Commissioned by Ludovico III Gonzaga, the church was begun in 1472 according to designs by Leon Battista Alberti on a site occupied by a Benedictine monastery, of which the bell tower (1414) remains.

The nave is roofed by a barrel vault, one of the first times such a form was used in such a monumental scale since antiquity, and probably modeled on the Basilica of Maxentius in Rome.

The massive dome (1732–1782) was designed by Filippo Juvarra, and the final decorations on the interior added under Paolo Pozzo and others in the late 18th and early 19th centuries.

[3] The purpose of the new building was to receive the pilgrims for the feast of Ascension when a vial, that the faithful believe contains the Blood of Christ, is brought up from the crypt below through a hole in the floor located directly under the dome.

Portions of the relic were extracted and taken by Charlemagne to the St Chapelle in Paris, and later to the Weingarten Abbey, to the Archbasilica of St. John Lateran in Rome, and to the Church of the Holy Cross in Guastalla[5] (built on behalf of Beatrix of Canossa[6]).

Alberti broke with basilican tradition by having multiple chapels branch off the nave instead of lining it with aisles—because the colonnades would block the view of ceremonies in the classic model.