Confined atomic systems are of great importance owing a multitude of possible applications in various areas of science and technology. Of particular interest are atoms encaged in the C60 molecule, A@C60, since the near-spherical symmetry of C60 simplifies theoretical studies, and the stability of C60 renders it amenable to experimental examination. A review of investigations of the electronic structure and dynamics of A@C60 is presented in this manuscript focusing on developments in the last decade. Addressed mainly are how the confinement affects electronic structure properties such as ionization potentials, localization of atomic electrons, Shannon entropy, correlation effects, relativistic interactions, and others. In the area of dynamics, photoionization and e-A@C60 scattering are reviewed and summarized, and the major effects of confinement on the dynamical properties, e.g., confinement resonances, hybridization, Wigner time delay, are delineated.