He reached the last 16 (second round) of the World Championship in 2005, after scoring the first 10–0 victory in the event since 1993 against 1993 semi-finalist James Wattana in qualifying. At the 2007 World Championship he beat Andy Hicks in the first round, 10–4, before beating World No. 1 and seven-time champion Stephen Hendry 13–6 to reach his first World Championship quarter-final and guarantee a place in the Top-16. Carter now has a 5–4 record against Hendry; conversely, he has only beaten Ronnie O'Sullivan in the 2nd round of the 2018 World Snooker Championship 13–9, having lost 16 of the last 17 encounters.