A century ago, nuclear physics entered astrophysics, giving birth to a new field of science referred to as "Nuclear Astrophysics". With time, it developed at an impressive pace into a vastly inter-and multidisciplinary discipline bringing into its wake not only astronomy and cosmology, but also many other sub-fields of physics, especially particle, solid-state and computational physics, as well as chemistry, geology and even biology. The present Astronuclear Physics review focusses primarily on the facets of nuclear physics that are of relevance to astronomy and astrophysics, the theoretical aspects being of special concern here. The observational aspects of astronomy and astrophysics that may have some connection to nuclear physics are only broadly reviewed, mainly through the provision of recent relevant references. Multi-messenger astronomy has developed most remarkably during the last decades, with often direct implications for nuclear astrophysics. The electromagnetic view of the components of the Universe has improved dramatically at all wavelengths, from the γ-ray to the radio domains, providing important new information on the Big Bang and the properties of stars. Neutrino astronomy has made giant steps forward. In particular, the famed "solar neutrino problem" is now behind us. The long-sought gravitational waves have at last been detected, with direct relevance namely to the merger of compact stars. The composition of Galactic Cosmic Rays and stellar/solar energetic particles is better known than ever, providing constrains on the GCR physics.On the stellar modeling side, we broadly brush the progress that has been made based on new observations, and even more so on the spectacular increase in computer capabilities. We briefly outline recent advances regarding the quiescent evolution of stars, as well as the eventual catastrophic supernova explosion of certain classes of them. In spite of significant improvements in the simulations, many long-standing problems still await solid solutions, particularly regarding the details and robustness of explosion simulations. In fact, new questions are continuously emerging, and new facts may endanger old ideas.The lion's share of this review concerns the nuclear physics phenomena that may be at work in astrophysical conditions, with a strong focus on theory. Exceptionally large varieties of nuclei have to be dealt with, ranging from the lightest to the heaviest ones, from the valley of nuclear stability all the way to the proton and neutron drip lines. An additional serious difficulty comes from the fact that the nuclei are immersed in highly unusual environments which may have a significant impact on their static properties, the diversity of their transmutation modes, some of which not being observable in the laboratory, and on the probabilities of these modes. The description of nuclei as individual entities has even to be replaced by the construction of an Equation of State at high enough temperatures and/or densities prevailing in the cores of exploding stars an...