The relativistic nucleus-nucleus collisions can produce hypernuclei and low-temperature hyper-matter as a result of hyperon capture by nuclear residues and free nucleons. We use the transport, coalescence and statistical models to describe the whole process, and point at the important advantages of such reactions: A broad variety of formed hypernuclei in masses and isospin allows for investigating properties of exotic hypernuclei, as well as the hypermatter both at high and low temperatures. The abundant production of multi-strange nuclei that can give an access to multi-hyperon systems and strange nuclear matter. The de-excitation of hot hyper-cluster will allow for the hyperon correlation studies. There is a saturation of the hypernuclei production at high energies, therefore, the optimal way to pursue this experimental study is to use the accelerator facilities of intermediate energies.