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The Greenhill area was the focus of large-scale Irish immigration in the second half of the 19th century – especially following the Great Famine – and from that period date the foundation of Greenhill's Roman Catholic Junior School and that of Saint Joseph's church, which was eventually to become the present-day Cathedral Church of Saint Joseph, designed by the firm of Pugin & Pugin and consecrated in 1888.
Greenhill contains Griffith John Street which close to the site of the birthplace of Doctor Griffith John
It is also known by locals as Brynmelyn (translation Yellow Hill) for the Public House (now closed) on Llangyfelach Street.
The combined effects of slum clearance schemes, damage to housing from wartime aerial bombardment in the Swansea Blitz, and post-war road improvement measures have led to some loss of identity for this once very densely occupied part of Swansea, to the extent that many locals now identify it simply as a part of the area lying to its immediate north and known as Brynmelyn (Welsh: "yellow hill"), after Bryn-Melyn Street, which traverses it. Note that Brynmelyn should not be confused with "Brynmelin", sometimes offered as a Welsh-language translation of Brynmill, which is an entirely different district of Swansea. Among nearby places are Cwmbwrla, Hafod, Manselton, Mayhill, and Swansea city centre.