Abstract <p>A key stage in off-line processing of the experimental HEP data is the reconstruction of trajectories (tracks) of the interacting particles from measurement data. For modern high-luminosity collider experiments, such as HL-LHC and NICA, a particular challenge for tracking is the very high, megahertz frequency of interactions, leading to an order-of-magnitude increase in the intensity of the data stream to be processed and, in addition, to a significant overlap of event track data when they are registered in track detectors. All these circumstances, recognized by physicists as the “Tracking Crisis,” have shown that the tracking algorithms already in use are not efficient, accurate, and scalable enough to handle data obtained in high-luminosity experiments. To overcome this crisis, in 2018, a group of physicists from CERN and other physics centers in the HEPTrkX project staged a TrackML competition to develop new solutions to tracking problems using deep neural networks. A data set for their training and testing was prepared and published on the Kaggle platform. The TrackML competition stimulated a lot of important research leading to the development of effective tracking algorithms based on graph neural networks, transformers, as well as the reanimation of tracking based on Hopfield neural networks, enhanced with computational means of adiabatic quantum computers. The experience in the development of tracking algorithms based on machine learning methods, accumulated during the last decade by the specialists from MLIT JINR, allowed them to actively engage in research on overcoming the problems of the tracking crisis not only by using the information from already published results, but also through original innovations, taking into account the specificity of domestic detectors in the high-luminosity experiments of the NICA megaproject at JINR. In the present report, we make a a brief review of the ongoing work and discuss its prospects.</p>