The only son of George Stephenson, Robert was born in Willington Quay. The following year his father moved to Killingworth. His first education was in the village school at Long Benton, but in 1814, he was sent to Bruce's Academy in Newcastle. He was also made a member of the Lit and Phil and received the invaluable assistance of the Rev. William Turner. In 1819, he was apprenticed to Nicholas Wood, the viewer at Killingworth Colliery.
In 1821 Robert helped his father on the Stockton-Darlington route survey and the following year spent six months at Edinburgh University, where he met George Parker Bidder, his lifelong friend. He then settled down to manage the locomotive factory on Forth Street, Newcastle, which his father had founded in 1823. His health was poor however, and he accepted an offer to superintend some gold and silver mines in Colombia. He returned in 1827, to find himself in the thick of the controversy over the traction to be used on the Liverpool Manchester line. Meanwhile Timothy Hackworth (q.v.) had taken a major step forward in locomotive design with his Royal George. Robert's Lancashire Witch recovered the lead, while the famous Rocket took shape under Robert's direction in Newcastle, and most of the subsequent design improvements were due to his skill. In 1828, he married Fanny Sanderson in London and took his bride to 5 Greenfield Place, Newcastle, now marked by a plaque. The period 1827-31, which yielded such splendid results, was the happiest in his career. He once remarked in London: 'It is the Robert Stephenson of Greenfield Place that I am most proud to think of.'
In 1833, Stephenson became engineer for the London Birmingham line, and was solely responsible for its success. This was the first railway into London, indeed the first trunk railway in the world, and had encountered formidable difficulties, notably the Blisworth cutting and the Kilsby tunnel. The line was completed in 1838, and, as Jonathan Glancey writes, its importance can hardly be exaggerated. It connected London with 'the workshop of the world' but also in effect with the 'Cottonopolis' of Manchester and the great port of Liverpool. It was intended principally for express passenger traffic and was described as 'unquestionably the greatest public work ever executed, either in ancient or in modern times.'
After that, Stephenson contended against Brunel in the 'battle of the gauges' and the struggle between the atmospheric and locomotion systems. From 1838, Robert Stephenson was engaged on railway work around the world, despite poor health and a chronic self-doubt. he wrote:

'I sometimes feel very uneasy about my position. My courage at times almost fails me and I fear that some fine morning my reputation may break under me like an eggshell.'

Robert Stephenson is best-known, perhaps, for his bridges. The splendid two-tier High Level of 1849 at Newcastle (many other designs, including Brunel's were rejected), the first road-rail bridge in the world, and the Royal Border Bridge (1847-50) at Berwick were two early successes. L.T.C. Rolt remarks:

'He who would measure imaginatively the magnitude of the Stephensons' achievement and seek to recapture something of the triumph and wonder of that heroic age of engineering, should stand upon the ruined castle keep at Berwick and gaze down that long, proud perspective of slender stone piers as the Flying Scotsman thunders across the water.'

The railway company celebrated these great feats with a dinner in Dobson's magnificent Newcastle Central Station, held under the first large vault of glass and iron ever constructed (by the Newcastle architect John Dobson). In his speech, Robert paid merited tribute to Thomas Harrison (q.v.) He refused a knighthood at this time, as his father did several times.
For the crossing of the Conway and the Menai Straits on the London-Holyhead line, Stephenson employed the tubular girder form which will always be linked to his name. Sir William Fairbairn (1789-1874), who had worked at the Percy Main Colliery from 1804 to 1811, and had become friendly with George Stephenson at that time, was closely concerned with the girder construction of the bridge. Stephenson also constructed the great Victoria bridge over the St Lawrence at Montreal, completed in 1859. It was for many years the longest bridge in the world. Robert Stephenson and Isambard Kingdom Brunel, the great rival of the Stephensons, became firm friends. Brunel was at Stephenson's side during the floating of the Conway and Menai tubes, giving support, just as Stephenson later helped and encouraged Brunel on the construction of the gigantic Great Eastern steamship. Robert Stephenson was buried in Westminster Abbey next to Telford, amid the mourning of the engineering world.