This paper addresses some of the of open problems in photonuclear physics which await to be resolved using high-brilliance γ-ray beams, such as precise measurements of total or partial cross sections of photonuclear reactions related to astroparticle physics and nuclear astrophysics. The readiness for such measurements at ELI-NP, as well as the state-of-the-art instrumentation which is available are discussed. The possibility to utilize γ-beams with orbital angular momentum in photonuclear experiments is addressed, too.