Robertson began his snooker career at a young age. Aged just 14, he became the youngest player to make a century break in an Australian ranking event. Then, when he was 17,^{[clarification needed]} he reached the third qualifying round of the World Championship.

In July 2003, Robertson won the World Under-21 Snooker Championship in New Zealand. This earned him a vital wildcard spot on the subsequent WPBSA Main Tour, where he is now an established figure. In 2003 he won the qualifying tournament for a wildcard place at the 2004 Masters, where he subsequently lost 6-2 to Jimmy White in the first round. Commentator John Virgo has recalled that Robertson already showed strong potting skills, but his game was limited in areas such as break-building and safety.

In 2004-2005, he moved up to the top 32 in the rankings, reaching the final stages of 6 of the 8 tournaments, despite having to play at least 2 qualifying matches for each one. He qualified for the final stages of the 2005 World Championship, losing 10-7 to Stephen Hendry in the first round. With Quinten Hann having also qualified, Australia had 2 players in the event for the first time since 1991.

In the 2005/2006 season, he continued to progress, moving up to the top 16 of the rankings at the end of the season. He reached 4 quarter-finals in the season, including the 2006 World Championships, in which he fought back from 12-8 down to level at 12-12 against eventual champion Graeme Dott, before losing the final frame by inadvertently potting the final pink, which he needed on the table in his attempts to snooker his Scottish rival.

He made his breakthrough in the 2006/2007 season. After finishing top of his group at the 2006 Grand Prix's round robin stage (he only lost one match: his opener against Nigel Bond by 3 frames to 2), Robertson then beat Ronnie O'Sullivan 5-1 in the quarter-finals of the event. So he went on to the semi-finals, being only the fourth Australian ever to do so in a ranking event. He beat Alan McManus 6-2 in the semis, to reach his first major final, where he faced a fellow first-time finalist, the unseeded Jamie Cope, whom he beat comfortably by 9 frames to 5 to win his first ever senior professional ranking tournament. The win earned Robertson £60,000, his highest amount of money earned in one tournament.

Robertson had early exits in both the UK Championship and the Saga Insurance Masters, but found his form again en route to the final of the Welsh Open 2007. He defeated Stephen Hendry 5-3, making a break of 141 in the last frame, then recovered from 4-3 down to beat Ronnie O'Sullivan 5-4 in the quarter-finals. He beat Steve Davis 6-3 in the semi-finals, and beat surprise package Andrew Higginson 9-8 in the final to take the title. He led 6-2 after the first session, then dropped six frames in a row to come within one frame of defeat, but took the remaining three frames to win the match.

He reached the second round of the World Championships, losing 13-10 to Ronnie O'Sullivan despite at one stage winning six frames in a row.

Robertson started 2007/2008 poorly, making early exits in three of the first four ranking events, plus the Masters and Malta Cup. He did reach the quarter-finals of the Northern Ireland Trophy after wins over Jamie Cope and Ian McCulloch. He finished the season ranked 10th, but outside the top sixteen on the one year list.

After a disappointing start to the 2008/2009 season, Robertson reached the final of the Bahrain Championship. He played Matthew Stevens, who had also been struggling for form for the previous few seasons. The match lasted almost 6 hours in total, with the Australian edging it by 9 frames to 7. This result has moved Neil back into the top 16, albeit provisionally. During the 2009 Masters Neil Robertson and opponent Stephen Maguire set a record of 5 consecutive century breaks. Robertson made 2 centurys, and Maguire made 3, with the 3rd sealing a 6-3 win over the Australian. At the 2009 World Championship Neil defeated Steve Davis, Ali Carter and Stephen Maguire to reach the semi-finals for the first time, before losing to Shaun Murphy.

During the snooker season, Neil is based in Cambridge, England. He practices at WT's Snooker Club with Joe Perry, who has spent 9 seasons among the world's top 32.