The present state of the problem of producing highly polarized systems of helium-3 by laser optical pumping over a broad temperature range is reviewed. The physical principles underlying the polarization of $^3$He nuclei during optical pumping and the exchange of metastability are described. Particular features of laser pumping at low temperatures are discussed. The possible use of polarized helium atoms in research on exchange and relaxation processes, in quantum magnetometry, and in nuclear physics to produce polarized targets and particle beams is discussed. The results of theoretical and experimental research on the quantum properties of highly polarized systems at low temperatures, near the temperature of quantum degeneracy, are reviewed.