This paper reviews the basic ideas as well as the latest experimental results obtained in the rapidly emerging field that studies macroscopic thermodynamic parameters and collective phenomena occurring due to exposure of matter to an intense ion beam. Beams of accelerated heavy ions as a tool to produce extreme states of matter under reproducible experimental conditions have attracted the attention of scientists from around the world. This is largely due to the fact that an ion beam releases its energy into the volume of matter. Importantly, relativistic colliders, being unique tools for probing extreme states of matter, have opened up new possibilities for producing various states of matter, including those exhibiting exotic sets of thermodynamic parameters. The problems addressed by experiments in the field are of fundamental nature and deal with equations of states of supercompressed matter, plasma phase transitions, critical points of metals, anomalous conductivity, noncongruent phase transformations, and atomic physics with strong interparticle interactions.