The façade, built abutting a pre-existing bell tower (1414), is based on the scheme of the ancient Arch of Titus. It is largely a brick structure with hardened stucco used for the surface. It is defined by a large central arch, flanked by Corinthian pilasters. There are smaller openings to the right and left of the arch. A novel aspect of the design was the integration of a lower order, comprising the fluted Corinthian columns, with a giant order, comprising the taller, unfluted pilasters. The whole is surmounted by a pediment and above that a vaulted structure, the purpose of which is not exactly known, but presumably to shade the window opening into the church behind it.
An important aspect of Alberti’s design was the correspondence between the façade and the interior elevations, both elaborations of the triumphal arch motif. The nave of the interior is roofed by a barrel vault, one of the first times such a form was used in such a monumental scale since antiquity, and quite likely modeled on the Basilica of Maxentius in Rome. Alberti most likely had planned for the vault to be coffered, much like the smaller barrel vault in the entrance, but lack of funds led to the vault being constructed as a simple barrel vault with the coffers then being painted on. Originally, the building was planned without a transept, and possibly even without a dome. This phase of construction more or less ended in 1494.
In 1597, the lateral arms were added and the crypt finished. 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.
The purpose of the new building was to contain the pilgrims who visited it during the feast of Ascension when a vial, that the faithful argue contains the Blood of Christ, is brought up from the crypt below through a hole in the floor directly under the dome. The relic, called Preziosissimo Sangue di Cristo ("Most Precious Blood of Christ"), is preserved in the Sacred Vessels, according to the tradition was brought to Mantua by the Roman centurion Longinus. It was highly venerated during the Renaissance. The shrines are displayed only on the Good Friday, to the faithful and then brought out along the streets of Mantua in a procession." (Text from Wikipedia).