After a private education at the Bruce Academy in Newcastle-upon-Tyne, an apprenticeship to Nicolas Wood, the manager of Killingworth Colliery, and a period at Edinburgh University, Robert went to work with his father on his father's railway projects, the first being the Stockton and Darlington. In 1823 Robert set up a company in partnership with his father and Edward Pease to build railway locomotives; the firm, Robert Stephenson & Company, built a large proportion of the world's early locomotives and survived into the mid 20th Century.
Robert did a good deal of the work for the Rainhill Trials-winning Rocket; following its success, the company built further locomotives for the Liverpool and Manchester Railway and other newly-established railways.
In 1833 Robert was given the post of Chief Engineer for the London and Birmingham Railway, the first railway to enter London. The line posed a number of difficult civil engineering challenges, most notably the Kilsby Tunnel, and was completed in 1838
He constructed a number of well-known bridges including the High Level Bridge at Newcastle-upon-Tyne, the tubular Britannia Bridge across the Menai Straits, a similar bridge at Conway, and the Royal Border Bridge at Berwick-upon-Tweed.
Robert Stephenson served as a Conservative member of parliament for Whitby from 1847 until his death. He was President of the Institution of Civil Engineers for two years from 1855. His remains are interred at Westminster Abbey.