  We present an overview of recent results and developments of the no-core
shell model (NCSM), an ab initio approach to the nuclear many-body problem for
light nuclei. In this approach, we start from realistic two-nucleon or two-
plus three-nucleon interactions. Many-body calculations are performed using a
finite harmonic-oscillator (HO) basis. To facilitate convergence for realistic
inter-nucleon interactions that generate strong short-range correlations, we
derive effective interactions by unitary transformations that are tailored to
the HO basis truncation. For soft realistic interactions this might not be
necessary. If that is the case, the NCSM calculations are variational. In
either case, the ab initio NCSM preserves translational invariance of the
nuclear many-body problem. In this review, we, in particular, highlight results
obtained with the chiral two- plus three-nucleon interactions. We discuss
efforts to extend the applicability of the NCSM to heavier nuclei and larger
model spaces using importance-truncation schemes and/or use of effective
interactions with a core. We outline an extension of the ab initio NCSM to the
description of nuclear reactions by the resonating group method technique. A
future direction of the approach, the ab initio NCSM with continuum, which will
provide a complete description of nuclei as open systems with coupling of bound
and continuum states, is given in the concluding part of the review.
