  Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular
technique for elucidating the three-dimensional structure of proteins and other
biologically significant complexes at near-atomic resolution. It is an imaging
method that does not require crystallization and can capture molecules in their
native states.
  In single-particle cryo-EM, the three-dimensional molecular structure needs
to be determined from many noisy two-dimensional tomographic projections of
individual molecules, whose orientations and positions are unknown. The high
level of noise and the unknown pose parameters are two key elements that make
reconstruction a challenging computational problem. Even more challenging is
the inference of structural variability and flexible motions when the
individual molecules being imaged are in different conformational states.
  This review discusses computational methods for structure determination by
single-particle cryo-EM and their guiding principles from statistical
inference, machine learning, and signal processing that also play a significant
role in many other data science applications.
