Deepening our knowledge of the partonic content of nucleons and nuclei represents a central endeavour of modern high-energy and nuclear physics, with ramifications in related disciplines such as astroparticle physics. There are two main scientific drivers motivating these investigations of the partonic structure of hadrons. On the one hand, addressing fundamental open issues in our understanding in the strong interactions such as the origin of the nucleon mass, spin, and transverse structure; the presence of heavy quarks in the nucleon wave function; and the possible onset of novel gluon-dominated dynamical regimes. On the other hand, pinning down with the highest possible precision the substructure of nucleons and nuclei is a central component for theoretical predictions in a wide range of experiments, from proton and heavy ion collisions at the Large Hadron Collider to ultra-high energy neutrino interactions at neutrino telescopes. This Article presents a succinct non-technical overview of our modern understanding of the quark, gluon, and photon substructure of nucleons and nuclei, focusing on recent trends and results and discussing future perspectives for the field.