The name is older than most Danish place names on record, and it has been spelled with remarkable inconsistency. Coins minted here from the reign of Canute the Holy (1080-86) through that of Svend Grathe (1146-57) carry Ranrosia, Ransias, Radrusia, Rand and Randrusia. Saxo Grammaticus wrote it in Latin as Randrusium; Snorri Sturluson's Heimskringla of 1230 gives the Icelandic Randrosi; Valdemar's Census Book of 1231 records Rondrus and Randrøs. Strip the variants back and you get two elements - rand, a hillside, and aros, a river mouth. Town on the hillside by the river mouth. The modern spelling only settled at the end of the 17th century. The description remains exact: Randers stands on the banks of the Gudenå about ten kilometres above its mouth in Randers Fjord, and it is Denmark's only natural river harbour.

The town was formally established around the 12th century, on ground already used in Viking times, and Canute IV minted his coins here while assembling men for an invasion of William the Conqueror's England. The 13th century treated the place badly: destroyed and rebuilt three times, including a burning in 1246 by the troops of Abel of Denmark during the uprising against his brother Eric IV. Market town privileges arrived in 1302 and trade followed. You can still trace the medieval defences without seeing a single stone of them - Østervold, Vestervold, Nørreport and Lille Voldgade curve through the centre in a ring, street names holding the line the walls once held. Some 170 merchants' estates stood here at the peak, and enough half-timbered building survives to make the old core legible: Sankt Mortens Kirke from the 15th century, Påskesønnernes Gård dating to 1460, and a neoclassical town hall finished in 1780.

Denmark in 1340 had no king. The whole country had been pledged to German counts, and the most powerful of them, Count Gerhard III of Holstein, was quartered in Randers. On 1 April, according to the story the town has told ever since, the nobleman Niels Ebbesen walked into a house in the town centre and killed him. The killing detonated a wider insurrection against German control. Ebbesen did not live to see how it ended - he died that December in a large battle at Skanderborg. His statue stands in front of the old town hall, which means that the figure presiding over the civic square of Randers is not a king, a bishop or a merchant, but a man remembered for an assassination.

Salmon fishing fed the medieval economy; the harbour and a competent shipbuilding and craft trade carried the town through prosperous 15th and 16th centuries. Then came the harder years - Swedish wars, plague and repeated fires through the second half of the 17th century - before the economy recovered, the harbour was extended, and by 1800 Randers was Jutland's largest town with 4,500 inhabitants. The gloves industrialised: Randers Handskefabrik was founded in 1811, among the oldest glove factories anywhere in the world, modernised under the Parisian glovemaker Charles Mattat, and by 1892 selling from shops in London and New York. The Vejrum family has owned it since 1927. Randers Handsker still keeps its headquarters and a shop in town, though production has long since moved abroad. Around the gloves grew heavier things: the Thor breweries from 1856, closed in 2003 with the brand now brewed elsewhere; the Hvide Mølle railway works of 1861, renamed Scandia in 1876, which built the IC3 intercity trains for Danish State Railways before Bombardier bought it in 2001.

Randers Kunstmuseum was founded in 1887 and now holds over 4,000 paintings, concentrated on Danish art of the 19th and 20th centuries. The Golden Age is well represented - Eckersberg, Christen Købke - and so is the quieter, stranger end of Danish painting, with Vilhelm Hammershøi's Interior with Young Woman Seen from the Back and several works by L.A. Ring, including Sommerdag ved Roskilde Fjord. The collection lives in Kulturhuset, a modernist building by the architect Flemming Lassen that also houses the cultural history museum and the city library. It was very nearly something else: in 2009 the practice 3XN won a competition for new premises of 7,550 square metres, and in September 2012 the project was abandoned after the money failed to materialise. So the paintings stayed where they were. There is something appropriate in a town that made its name on gloves keeping its Hammershøi in a well-built modernist box rather than a signature landmark - Randers has never much traded on spectacle. Today about 64,764 people live here, and the biggest draw is a rainforest under glass.