The exact treatment of nuclei starting from the constituent nucleons and the fundamental interactions among them has been a long-standing goal in nuclear physics. In particular, nuclear scattering and reactions require the solution of the many-body quantum-mechanical problem in the continuum, and thus represent an extraordinary theoretical as well as computational challenge for ab initio (i.e., first principle) approaches. Due to the advent of new theoretical techniques and exceptional improvements in computational capabilities, ab initio calculations are now beginning to address nuclear reactions among light nuclei. Yet, the field is still in its infancy, and we have a great deal more to learn in order to understand light-ion fusion reactions, but also light exotic nuclei, for which most low-lying states are unbound, so that a rigorous analysis requires scattering conditions. I will present one of such new techniques, an ab initio many-body approach, which derives from the combination of the ab initio no-core shell model with the resonating-group method, and I will review recent results for neutron and proton scattering on s- and light p-shell nuclei using realistic nucleon-nucleon potentials. In conclusion, I will outline the progress toward the treatment of deuterium-nucleus scattering and transfer reactions.