The 1/2-BPS index of N=4 SYM with gauge group U(N) can be written as the large N answer times an infinite series of finite N corrections. This expansion is called the giant graviton expansion. I will explain how such an expansion arises in the bulk as a result of the localization of the path integral which computes the bulk 1/2-BPS index to a product of small fluctuations of the vacuum and of the collective modes of an arbitrary number of maximal giant gravitons.