Munich is famed for its Bavarian history, but it's also at the front of some cutting-edge technology. There's no greater example of this than BMW-Welt & Museum, a futuristic silver building dedicated to the techinical wizardry of the famous motoring group. Germany won the FIFA World Cup in 2014 and there's no better place to witness the skill and passion for the game than at Allianz Arena, with a fully color-changing exterior.
There older, much older architectural landmarks that have made the city what it is. You can't miss the twin-domed Gothic cathedral, rebuilt after war damage. You can climb to the top of the bell tower at the Gothic church Kirche St. Peter, and see a performance in the neo-classical Bayerische Staatsoper.
Even in its art scene, it's often the building itself which is as much an appeal as the content. Take Museum Brandhorst, opened in 2009, with its multicolored façade, and the concrete-and-glass Pinakothek Der Moderne. To get a panorama of the city, from its red roofs to domes and gargoyles and modern structures, you won't do much better than climbing to the top of Neues Rathaus, to see the city unfold.