This talk considers provable methods for cryo-electron microscopy, which is an increasingly popular imaging technique for reconstructing 3-D biological macromolecules from a collection of noisy and randomly oriented projection images, with applications in e.g., drug design. The talk will present two uniqueness guarantees for recovering these structures from the second moment of the projection images, as well as two associated numerical algorithms. Mathematically, the results boil down to ensuring unique solutions to highly structured non-linear equations.