[1] The cathedral was built in the late nineteenth century and is located in the Greenhill area of Swansea.

Originally built as a church, St Joseph's was conceived by Father Wulstan Richards, OSB who came to Greenhill in 1875.

Built as a church, it was converted to a cathedral in 1987 for the redefined Diocese of Menevia.

[3] The plan of the building is that of an apsidal chancel flanked by side chapels with a seven-bay aisled nave, a polygonal tower with spire in the north-west corner and twin porches on the western facade.

The cathedral has a modern pantile roof and there is a gabled parapet, topped with a finial on the western side of the building above a small arched opening over a four-light Geometric traceried window.