Ultracold ions is one of the most successfully developing physical platforms in the field of quantum computing: long coherence time and high gate fidelities ensured its leadership in terms of quantum volume (2²¹) compared to other systems, such as a superconducting platform (the maximum demonstrated quantum volume is 2⁹). The deepest benchmarking algorithms to date have been executed on ion quantum computers and error correction codes have been successfully demonstrated, opening up the prospects for transitioning from the current era of noisy intermediate-scale quantum processors (NISQ) to the next epoch. In Russia, the field of ion quantum computers began to develop with the launch of the Roadmap for Quantum computing in 2020. In this review, we present the basic principles of ion quantum computer operation, an overview of current world achievements in this area, as well as the main results of our group obtained during the implementation of the Roadmap.