In this paper, we present the results of the transport, coalescence and statistical model calculations to describe the production of hypernuclei and study their properties in relativistic nucleus-nucleus collisions. Such hypernuclei and low-temperature hypermatter can be produced as a result of hyperon capture by nuclear residues and free nucleons. The dynamical reaction stage leading to the strangeness production is described within the transport cascade and UrQMD models. Large excited hypernuclear species can be formed from target and projectile residues in peripheral collisions. To describe its following evolution at high excitation energies we have generalized the statistical multifragmentation model (SMM) on hypernuclei, as well as the evaporation, fission and Fermi-break-up models at low energies. We calculated the yields, the mass with isotopic distributions of produced nuclei and hypernuclei, and found important regularities and correlations. We have also established how the binding energies of hypernuclei can be evaluated via the comparison of isotope yields. Our approach can be used also for multistrange nuclei. We have extended the coalescence model for the formation of excited hyperclusters from individual baryons in the central collisions. De-excitation of hot coalescence clusters presents a novel mechanism for the hypernuclei production and shows new possibilities for their investigation.