Abstract : We discuss the mathematics related to two important methods in molecular imaging - X-ray crystallography and cryo-electron microscopy (cryo-EM). In X-ray crystallography a molecule is bombarded with an X-ray beam and the diffraction pattern is measured. In Cryo-EM a sample such as a protein is flash frozen in a liquid solution and then bombarded with a low intensity electron beam, and the projection onto a plane is measured. In both of these experiments the problem of recovering a structure from the experimental measurements can be viewed mathematically as understanding the intersection of the orbit of a compact group with a linear subspace or collection of linear subspaces. In the case of crystallography the mathematical problem is called the phase retrieval problem and the group is the torus $(S^1)^n$. In the case of cryo-EM the mathematical problem is called the multi-reference alignment (MRA) problem and the groups are products of orthogonal groups.