It is know that face images of different people lie on multiple low-dimensional subspaces. In this talk, we will show that these subspaces are tightly bundled together as a "bouquet". Precisely due to this unique structure, it allows extremely robust reconstruction and recognition of faces despite severe corruption or occlusion. We will show that if the image resolution and the size of the face database grow in proportion to infinity, computer can correctly and efficiently recover or recognize a face image with almost 100% of its pixels randomly and arbitrarily corrupted, a truly magic ability of L1-minimization. This is joint work with John Wright of UIUC.