The cryopreservation of human spermatozoa has been an option for patients undergoing chemo or radiotherapies since the late 1950s. Presently, there are different techniques for the cryopreservation of spermatozoa. The most commonly used techniques are programmable slow freezing and freezing on liquid nitrogen vapors, while the use of vitrification is still not accepted as clinically relevant. Although there have been many improvements, the ideal technique for achieving better post-thaw sperm quality continues to be a mystery. A major obstacle during cryopreservation is the formation of intracellular ice crystals. Cryodamage generated by cryopreservation causes structural and molecular alterations in spermatozoa. Injuries can happen because of oxidative stress, temperature stress, and osmotic stress, which then result in changes in the plasma membrane fluidity, motility, viability, and DNA integrity of the spermatozoa. To prevent cryodamage as much as possible, cryoprotectants are added, and in some clinical trial cases, even antioxidants that may improve post-thaw sperm quality are added. This review discusses cryopreservation techniques, cryodamage on molecular and structural levels, and cryoprotectants. It provides a comparison of cryopreservation techniques and describes recent advances in those techniques.