Brandenburg is built on islands and between them. For centuries it was not one town but three: the Altstadt on the western bank, the Neustadt on the eastern, and the cathedral district on its own island, the Dominsel, each with its own government and its own defences. The Old and New Towns both joined the Hanseatic League in 1314–15, yet they merged into a single municipality only in 1715, and the cathedral district was not folded in until 1928. Water is still the organising fact of the place. Vessels working the Havel — a European waterway — choose between the old Brandenburg City Canal, four kilometres straight through the middle of town and down through the city lock, now given over to leisure craft, and the Silo Canal skirting the eastern and northern fringes, which is where the commercial barges go.

The foundation stone of the cathedral of St Peter and Paul was laid on the Dominsel in 1165, and the building was consecrated five years later with Albert the Bear and his sons present. Begun Romanesque, finished Gothic in the fourteenth century, it is severe from outside — almost blank. Inside is another argument entirely. The Bunte Kapelle, the Coloured Chapel, carries a painted vault that ambushes anyone who came expecting brick austerity, and the Wagner organ of 1725 is among the most celebrated baroque instruments in Germany. Judith of Poland, who died sometime in the 1170s, lies buried here. Berlin took the capital of the margraviate in 1417 and the court left for Potsdam after the Thirty Years' War, but the cathedral went on regardless, outlasting every institution that had once made this the centre.

In front of the Old Town Hall stands a sandstone knight 5.35 metres tall, put up in 1474. Rolands like him were raised across northern Germany as declarations that a town answered to itself rather than to its bishop or its lord — a statue functioning as a legal argument, planted where everyone had to walk past it. The town hall behind him is late Gothic brick with stepped gables and an ornate portal. Two churches make the same material sing: St Catherine's, finished in 1401 in the New Town, and St Gotthardt's a few years later, both of them textbook north German brick Gothic. Four watchtowers survive from the medieval wall — Steintorturm and Mühlentorturm in the New Town, Rathenower Torturm and Plauer Torturm in the Old.

By the late nineteenth century this was heavy industry country. Steelworks arrived, then bicycles — Brennabor, Corona and Excelsior were all built here — then a toy industry, and between the wars an enormous Reichsbahn railway complex at Kirchmöser. In 1934 the Arado aircraft company opened a satellite factory in Brandenburg that was turning out trainers and other machines for the Luftwaffe by 1935. That factory is a large part of the reason Allied bombers came, and why 70 percent of the town lay destroyed by 1945. The Nazi years left more than rubble behind. One of the first concentration camps in Germany opened on Neuendorfer Straße in 1933; later, at the old Görden jail, the regime murdered disabled adults and children in some of its first killings by gas, and applied what it learned there at Auschwitz and the other extermination camps. Those victims were people the state had decided it could dispose of. The site is now a memorial.

Vicco von Bülow was born here on 12 November 1923 and became, as Loriot, the most quoted comic mind in postwar Germany — a cartoonist and film-maker whose bulb-nosed figures conduct themselves with catastrophic dignity, and whose lines are still traded across German dinner tables. He was made an honorary citizen of Brandenburg in 1993 and kept the title until his death in 2011. The town he came from has had a hard few decades: the population fell from roughly 100,000 in 1989 to about 75,000 by 2005, the departures overwhelmingly young. What remains is a working small city with its own theatre and symphony orchestra, a tram network at the heart of its transport, an industrial museum that anchors the European Route of Industrial Heritage, and an archaeological museum installed in a former monastery church.