The band became popular in the Welsh-language music scene in 1998, following the release of their first album, Sombreros yn y Glaw (Sombreros in the Rain), on the Crai label. In 1994 they won both the Urdd and the National Eisteddfod best band awards. Since forming in 1991, the band have supported Yr Anhrefn, Super Furry Animals, Gorky's Zygotic Mynci, Stereophonics, Catatonia and Geraint Jarman. To coincide with their first album (Sombreros yn y Glaw), the band recorded a video for the i-Dot music programme on S4C, for the song Fan Hyn (Right Here).
Toms also went on to form Mim Twm Llai, and was voted best composer at the 2002 and 2003 Radio Cymru awards. Roberts was also a member of Sibrydion, and later ran Cell, a recording studio, education centre and live music venue in Blaenau Ffestiniog.
Anweledig played their final at the Queens Hotel, Blaenau Ffestiniog the day after the 2008 Box, almost 16 years since the start of the band.