  The nuclear shell model has been perhaps the most important conceptual and
computational paradigm for the understanding of the structure of atomic nuclei.
While the shell model has been predominantly used in a phenomenological
context, there have been efforts stretching back over a half century to derive
shell model parameters based on a realistic interaction between nucleons. More
recently, several ab initio many-body methods---in particular many-body
perturbation theory, the no-core shell model, the in-medium similarity
renormalization group, and coupled cluster theory---have developed the
capability to provide effective shell model Hamiltonians. We provide an update
on the status of these methods and investigate the connections between them and
potential strengths and weaknesses, with a particular focus on the in-medium
similarity renormalization group approach. Three-body forces are demonstrated
to be an important ingredient in understanding the modifications needed in
phenomenological treatments. We then review some applications of these methods
to comparisons with recent experimental measurements, and conclude with some
remaining challenges in ab initio shell model theory.
