Vortex light beams, that possess a helical phase front and carry nonzero projection of the orbital angular momentum (OAM) on their propagation direction, attract currently much attention in many areas of modern physics. They are considered, for example, as a valuable tool in high-resolution microscopy, classical and quantum information transfer as well as for manipulation of microparticles and even Bose–Einstein condensates. During the recent years, moreover, a particular emphasis was also placed on the interaction of vortex light modes with single trapped atoms or ions. In my talk, I will give an overview of experimental and theoretical atomic physics studies with vortex light. In particular, we will consider how the coupling of OAM modes with atomic systems can modify both the (conventional) selection rules and the relative strength of multipole transitions. Moreover, the operation of strongly forbidden atomic transitions by OAM photons will be also discussed in detail. Some of these transitions are discussed as candidates for novel frequency standards, and, thus, the use of twisted light may help in development of new generation of atomic clocks. This colloquium talk is dedicated to the celebration of the 60th birthday of Professor Stephan Fritzsche.