Robertson, together with Old Tom Morris, worked on the design and improvement of several courses, including modifications to the Old Course, St Andrews and extending the Carnoustie Links.

At a time when golf was predominantly played by well-off gentlemen, the 1830s and '40s saw the arrival of a new category of golfer, the "playing professional." Robertson was the most famous of this new breed, and was generally regarded as the best golfer in the period 1840 to 1860.

Professionals, like Robertson, typically made a living from playing for stake money, ball and club making, caddying and providing instruction. It is said Robertson was never beaten when playing for money. In 1843 a marathon 20-round challenge match between Robertson and Willie Dunn Sr of Musselburgh was arranged to establish who was the top golfer of the time. Robertson come out the winner. Not only the top professional, Robertson was also considered the premier ball and club maker of his time.

Old Tom Morris worked for Robertson as an apprentice, and the two formed a near invincible playing partnership in challenge matches. However, they rarely competed against each other, respecting the apprentice-master relationship. This lack of competition between them put a question mark against the question of who was really the best player, Robertson or Morris? The relationship between them soured when Robertson fired Morris when he caught him using a gutta-percha ball; Robertson's business was based on making the older featherie ball. Robertson's attempts to suppress the popularity of the new and cheaper "guttie" were ultimately unsuccessful, hastening the demise of the family's 100-year-old business making the "featherie." Robertson eventually switched to making "guttie" balls.

Robertson died in 1859 following an attack of jaundice. He is buried in the grounds of St Andrews Cathedral. The Open Championship (golf's oldest major), came about as a result of the void left by Robertson's death. In 1860, professional golfers gathered in Prestwick to find Robertson's successor as the "Champion Golfer". That honour was surely shared between Willie Park Sr (Open Championship winner in 1860, '63, '66, '75) and Old Tom Morris (winner in 1861, '62, '64, '67).