Results of experimental studies of the Х-pinch since its invention and implementation in 1982 at the Lebedev Physical Institute are presented. The concept of the Х-pinch arose in the course of innovative experiments on studying the generation of hot dense plasma in nanosecond Z-pinches. The main idea was to localize the region occupied by the plasma and stabilize the moment of its formation. This was achieved by using a load in the form of crossed wires. The resulting plasma object turned out to be so interesting that a new scientific direction appeared in plasma physics. At present, studies in this direction are being performed in many laboratories worldwide. The term Х-pinch became conventional, and sections devoted to its study are always present at plasma conferences. Х-pinch is not only a very interesting scientific object, but also a unique source of X-ray emission with extreme parameters. The use of Х-pinches for point-projection X-ray radiography of high-energy-density objects provided many new experimental results. In some cases, the concepts of the processes occurring in matter upon fast energy deposition changed dramatically. The review consists of two parts. The first part briefly outlines the history of creation and studies of Х-pinches, describes the diagnostic techniques and devices developed during these studies, and presents the main results obtained in studying the physical processes occurring in the Х-pinch. The second part is devoted to the results of detailed studies of the Х-pinch hot spot-the region where the highest plasma parameters are achieved and which is a source of X-ray emission with extreme parameters. Some results of Х-pinch simulations are also presented.