Stevens became a professional snooker player in 1994; in his second season, he won the Benson & Hedges Championship to qualify for the Masters, where he beat Terry Griffiths 5–3 but lost 5–6 to Alan McManus.

He also reached the quarter-finals on his debut at the Crucible in the World Championship, beating Alain Robidoux and Mark King before losing to Ken Doherty.

In 2002, he looked certain to have won a place in the final, leading Peter Ebdon 16–14 in their semi-final tie, and just needing a relatively simple red in the 31st frame to leave his opponent requiring snookers.

[citation needed] The following year, Stevens was beaten by Ken Doherty 8–13 in the second round of the 2006 World Championship, having gone into the final session level at 8–8.

In 2008, he was defeated in the first round of the World Championship for the first time in his career, by defending champion John Higgins, and he finished ranked outside the top 16 for the second consecutive season.

The only highlight of the 2008–09 season was a run to the final of the Bahrain Championship, in which he was given a top 16 seeding due to the unavailability of three leading players.

He also lost a close match 9–10 to Marcus Campbell in the 2010 World Championship qualifiers, and thus did not make it to the main draw at The Crucible for the second year in succession.

Stevens made a promising start to the 2010–11 season by qualifying for the Shanghai Masters with a 5–2 victory over Anda Zhang.

He whitewashed number 5 seed Shaun Murphy 4–0 in the last 32, and in the last 16 he beat fellow Welshman and close friend Ryan Day 4–3.

[5] After losing in the first round of the Australian Goldfields Open to Liang Wenbo, Stevens reached the quarter-finals of the Shanghai Masters by defeating Stephen Lee and Martin Gould.

[6] A last 16 exit in the 2011 UK Championship to Ding Junhui followed, before Stevens reached his second ranking event quarter-final of the season in the German Masters courtesy of 5–1 victories over both Craig Steadman and Neil Robertson.

[7] Due to being ranked inside the top 16, Stevens played in his first Masters tournament since 2007 during the season and was beaten by John Higgins 2–6 in the first round.

[13][14] At the 2012 UK Championship he beat Dominic Dale 6–1 and Marco Fu 6–4 to reach the quarter-finals for the first time since lifting the trophy in 2003.

[15] Stevens missed a simple brown at 4–1 up against Mark Williams in the first round of the Masters and then made a series of errors during the rest of the match to lose 4–6.

[16] His second quarter-final of the season came at the German Masters, where he was defeated 3–5 by Marco Fu, before losing 2–4 to Stephen Maguire in the second round of the Welsh Open.

[14] Stevens travelled to Haikou, China, for the World Open, but his cue failed to arrive on time for his first round match against David Gilbert.

[17] It was Trump this time who suffered cue troubles as his tip became damp during the match and Stevens took full advantage to triumph 5–3.

[14][21] At the season's opening ranking event, the 2013 Wuxi Classic, Stevens beat Lu Ning 5–1, Liang Wenbo and Peter Lines both 5–3, and David Morris 5–2, to advance to the semi-finals.

[27] At the 2014 Australian Goldfields Open, Stevens reached his first quarter-final in a year by knocking out Luca Brecel 5–3 and Fergal O'Brien 5–3, but lost 2–5 to Xiao Guodong.

[28] He was eliminated 2–6 by John Higgins in the third round of the UK Championship, but reached the last 16 of the Welsh Open by recording his first victory over Ronnie O'Sullivan in twelve years, recovering from 0–2 down to win 4–3.

At the UK Championship, he beat James Cahill 6–1, Michael White 6–4, and Joe Perry 6–2,[34] but his run ended with a 2–6 loss to Ronnie O'Sullivan.