The club's historic home ground was Stradey Park in Llanelli, but they moved in 2008 to the new Parc y Scarlets in adjacent Pemberton.

After attending a Good Friday service in chapel, a group of young athletes from Llanelli met to discuss the formation of a new rugby club in the area.

In September 1879, it was announced that the club were to move from People's Park, having acquired the Stradey cricket ground for their practices and matches.

Players who wore the Scarlet jersey in this pre-war era included Albert Jenkins, who scored over 121 tries for the club as a centre.

Players at Llanelli during the 1970s included Ray Gravell, Gareth Jenkins, Delme Thomas, Phil Bennett, and Derek Quinnell; and the team was coached by Carwyn James and assisted by former captain and Wales international hooker Norman Gale.

"9–3" is a poem by Welsh comedian and singer Max Boyce and refers to the match between Llanelli and the New Zealand All Blacks at Stradey Park in front of 26,000 supporters on 31 October 1972.

A long distance Andy Hill penalty ensured Llanelli emerged victors by 9–3 and the crowd famously ran onto the pitch at the end and carried off players such as Delme Thomas.

With players such as Ieuan Evans amongst the squad, Llanelli won the Welsh Cup five times in eight years between 1985 and 1993 including in consecutive seasons in 1991,1992 and 1993.

The late 1990s and early years of the 21st century also produced many Welsh internationals including Rupert Moon, Ricky Evans, Wayne Proctor, Scott Quinnell and Stephen Jones.

On 28 March 2023, Llanelli RFC announced their withdrawal from the Premier Division for the 2023–24 season, as they would be unable to field a team in the expanded league.

[3] Llanelli RFC would instead seek to arrange friendlies as a development side for the Scarlets, and look to join a proposed eight–team league above the Premier Division.

[4] Llanelli did not join the new competition, Super Rygbi Cymru, with Carmarthen Quins and Llandovery representing the Scarlets region.

[5] As a link to the club's team anthem Sosban Fach, there were sosbenni on top of the uprights of both sets of posts at Stradey Park.

When Llanelli RFC play Bath, it was tradition that a rag doll was hung from the crossbar, which the winning team then kept until their next encounter.