The Cryo-electron microscopy (Cryo-EM) reconstruction problem is to recover a 3D structure of a molecule from 2D images, in the presence of high noise levels and in the absence of information about the relative orientations of the images. In many cases, the problem is further complicated by heterogeneous samples, containing a variety of molecules. I will talk about approaches to classification and discuss a simultaneous classification and determination of relative orientations using semidefinite programming (SDP).