T-dualization can be thought of as a procedure for replacing a principal torus bundle with some object which ''approximates'' a principal dual-torus bundle, in such a way that the two objects have isomorphic K-theory. I will briefly point out some areas of string theory in which T-duality arises, but will focus on the dualization procedure itself and on understanding the T-dual objects. T-duals are interesting geometrically because it turns out that dualization produces not a dual-torus bundle but a gerbe on a dual-torus bundle, and once gerbes are involved noncommutative tori also appear. Thus the geometric problem of replacing torus fibers in a bundle by dual torus fibers naturally brings into play stacks and gerbes as well as noncommutative geometry.