One of the main directions of the scientific research at the Joint Institute for Nuclear Research (JINR) in Dubna is the relativistic nuclear and spin physics. The new JINR flagship program in this direction is now realized within the project NICA (Nuclotron-based Ion Collider fAcility). The main goal of the NICA scientific program is an experimental study of hot and dense strongly interacting matter in heavy ion collisions at nucleon-nucleon centre-of-mass energies of 4-11 GeV and at average luminosity of 1027 cm−2 s −1 for Au (79+) in the collider mode. In parallel, fixed target experiments at the upgraded JINR superconducting synchrotron Nuclotron are carried out with the extracted beams of various nuclei species up to gold with the momenta up to 13 GeV/c for protons. The program also foresees a study of spin physics with extracted and colliding beams of polarized deuterons and protons at the center-of-mass energies up to 26 GeV for proton collisions. The proposed program allows to search for possible signs of the mixed phase and critical endpoint, and to shed more light on the problem of nucleon spin structure. The survey of the main directions of the JINR scientific research program and general design and construction status of the NICA complex are presented.