Västerås Stadsmuseum covers the city's history from its Viking-era origins through industrialisation to the present. Housed in a historic building near the castle, it has a strong section on the ABB and ASEA industrial legacy — Västerås was the headquarters of the Swedish engineering empire that became ABB, and the machinery, models, and photographs document a genuinely important chapter in Swedish industrial history.
The Viking and medieval sections are solid too, with finds from the Anundshög area and objects from the cathedral's archives. Combined with the cathedral and castle, it makes for a good half-day circuit of the old town's history.