The actual dedication is not to St Joseph the Patriarch, but to St Joseph Calasanctius (or de Calasanz) who was a Spanish priest involved in educational work in Rome. However, the former is also venerated here.
The church is sometimes referred to as San Giuseppe Calasanzio, but not by the Diocese.
It was designed by Andrea and Carlo Busiri Vici, and built in 1888 for the Suore di San Giuseppe Calasanzio. This was a sisterhood inspired by the patron saint, which now seems to be extinct.
In 1910, the complex was sold to the newly-founded Polish Pontifical Institute (Polski Papieski Instytut Kościelny), a seminary for training Polish priests.
The church remains part of the seminary, but is a subsidiary church of the parish of Sacro Cuore di Gesu in Prati and so is not a private chapel.
The diminutive façade, in thin bricks of a light purplish colour, is inserted into (and dwarfed by) a much larger and higher building which is rendered in a yellow ochre. The effect is quite odd.
The ornate entrance has a marble doorcase which is decorated with a carved vine. Above this is an exterior aedicule consisting of three brick arches, the middle one being higher, supported by four little marble columns in the round with vaguely Corinthinan capitals. These columns are supported by corbels inserted just above the lintel. Above the arches is a gable with a projecting stone cornice supported by little capitals. This aedicule contains mosaics of St Joseph (the patriarch, not Calasanctius) holding the Christ Child and being venerated by two angels.
Above the entrance the façade is blank brickwork, except for an ornate round window with a dentillated brick frame in relief and stone fenestration in the form of a cross over a circle. Above this is an equally ornate horizontal cornice with dentillation, supported by a line of little brick arches on stone corbels.
To either side of the main portion of the façade are two matching side portions which only reach as high as the round window. Unlike the main portion they have two storeys. The first storey of each has two brick pilasters supporting a dentillate cornice and flanking a round-headed window decorated with a dentillate stone arc. The second storey, which is not as high, also has two pilasters supporting a cornice in the same style as that of the main portion. They flank two small arched windows separated by a little marble pillar.
The otherwise bare white interior has a small external sanctuary apse, and this has recently been decorated with a mosaic by Marko Ivan Rupnik showing Chrish in glory. This apse contains two round-headed windows, and these have modern semi-figurative stained glass which is part of the artwork. They feature Our Lady and St John the Evangelist, thus the work as a whole is Deesis.
The triumphal arch also bears a mosaic, with St John the Baptist on the left and St Joseph (?) on the right.