The dedication was to St Andrew the Apostle.
The building started its career as the Basilica of Junius Bassus, a civic basilica erected by the consul of the same name who served in the year 331.
It was transformed into a church in the late 5th century under Pope Simplicius, and was the first church dedicated to St Andrew in the city.
The odd surname dates at least from the 8th century, and may refer to the foundress named Barbara of a monastery next to the church (the first reference gives the fuller version of Catabarbara Patricia). The monastery was associated with that at Sant'Antonio Abate all'Esquilino next door, and was part of the service complex of Santa Maria Maggiore.
However, the church fell out of use in the 17th century and was noted as ruinous in 1686. Fortunately, several palaeochristian epigraphs were transcribed before the remains were concealed by later building work.
The end came when the Pontifical Oriental Institute was built on the site in 1930. The ruins were exposed, recorded and then demolished with some decorative fragments being preserved in museums.
The building was a simple rectangular structure, with an apse and a narthex or portico with rounded ends.
The interior was lavishly decorated with opus sectile work, which is like a mosaic except that the pictures are built up from larger, shaped pieces of coloured stone.
There was an inscription in the apse commemorating the dedication by Pope Simplicius, as well as a mosaic of Christ the Teacher (a drawing of this is extant).
Fragments of the opus sectile are to be found in the Museo dei Conservatori and in the Museo Nazionale Romano in the Palazzo Massimo.
The mosaics preserved in the Institute are not from this church, but from an adjacent ancient private house excavated with it in 1930.