Since the time of Noether, mathematicians have learned the lesson that when faced with a class of structures, it is almost always fruitful to consider the structure-preserving maps: in other words, to work with a category rather than a mere set or class. More recently, it has been realized that it is often useful to go further: don't just take objects and maps between them, but also maps between maps, maps between maps between maps, and so on. This is not obvious (what is a map between maps, anyway?) but turns out to be an idea of incredible fertility. I will concentrate on what happens when you go just one step further, from ordinary categories to 2-categories or bicategories. I will also explain how the bicategorical approach sheds light on the notion of Morita equivalence.