Interaction of atoms with twisted light Twisted photons are particles which carry a nonzero projection of the orbital angular momentum onto their propagation direction. During the last years the interaction between twisted photons and atoms became an active area of fundamental and applied research. In the present work we show how the “twistedness” of Bessel and Laguerre Gauss photons may affect a number of fundamental light matter interaction processes in comparison with the results for standard plane wave radiation. In particular we perform an analysis of the photoionization of hydrogen molecular ions by twisted photons. It is shown that the oscillations in the angular and energy distributions of photoelectrons are affected by the intensity profile of twisted photons. We also investigate the excitation of atoms by these twisted photons. We demonstrate here that the orbital angular momentum of light leads to the alignment or specific magnetic sublevel population of excited atoms. Apart from these studies we explore the elastic Rayleigh scattering of twisted photons by hydrogenlike ions. Our results indicate that the “twistedness” of incident photons may significantly influence the polarization properties of scattered light.