\textit{Ab initio} theories of nuclear structure and reactions

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 addition to the complex nature of nuclear forces with two-nucleon, three-nucleon and possibly even four-nucleon components, one faces the quantum-mechanical many-nucleon problem governed by an interplay between bound and continuum states. In recent years, significant progress has been made in \textit{ab initio} nuclear structure and reaction calculations based on input from QCD employing Hamiltonians constructed within chiral effective field theory. I will discuss recent breakthroughs that allow for \textit{ab} \textit{initio} calculations for ground states and spectroscopy of nuclei throughout the $p$- and \textit{sd}-shell and beyond with two- and three-nucleon interactions. I will highlight results obtained within the NCSM, CCM, QMC, and nuclear lattice EFT. I will also present new \textit{ab initio} many-body approaches capable of describing both bound and scattering states in light nuclei simultaneously and discuss results for reactions important for astrophysics, such as $^{7}$Be(p,$\gamma )^{8}$B radiative capture, and for $^{3}$H(d,n)$^{4}$He fusion.