Motivated by limitations of the Bloch-Horowitz-Brandow perturbative approach to nuclear structure we have developed the non-perturbative ab initio no core shell model (NCSM) capable of solving the properties of nuclei exactly for arbitrary nucleon-nucleon (NN) and NN+ three-nucleon (NNN) interactions with exact preservation of all symmetries. We present the complete ab initio NCSM formalism and review highlights obtained with it since its inception. These highlights include the first ab initio nuclear-structure calculations utilizing chiral NNN interactions, which predict the correct low-lying spectrum for 10B and explain the anomalous long 14C β-decay lifetime. We also obtain the small quadrupole moment of 6Li. In addition to explaining long-standing nuclear structure anomalies, the ab initio NCSM provides a predictive framework for observables that are not yet measured or are not directly measurable. For example, reactions between short-lived systems and reaction rates near zero energy are relevant to fusion research but may not be known from experiment with sufficient precision. We, therefore, discuss, in detail, the extension of the ab initio NCSM to nuclear reactions and sketch a number of promising future directions for research emerging from the NCSM foundation, including a microscopic non-perturbative framework for the theory with a core. Having a parameter-free approach, we can construct systems with a core, which will provide an ab initio pathway to heavier nuclei.