In tissue and organ transplantation, it is of great importance to avoid the transmission of blood-borne viruses to the recipient. While serologic testing for anti-human immunodeficiency virus (HIV)-1 and -2, anti-hepatitis C virus (HCV), hepatitis B surface antigen (HBsAg), anti-hepatitis B core antigen (HBc), and Treponema pallidum infection is mandatory, there is until now in most countries no explicit demand for nucleic acid amplification testing (NAT) to detect HIV, hepatitis B virus (HBV), and HCV infection. After a review of reports in the literature on viral transmission events, tissue-specific issues, and manufacturing and inactivation procedures, we evaluated the significance of HIV, HCV, and HBV detection using NAT in donors of various types of tissues and compared our results with the experiences of blood banking organizations. There is a significant risk of HIV, HCV, and HBV transmission by musculoskeletal tissues because of their high blood content and the high donor-recipient ratio. If no effective virus inactivation procedure for musculoskeletal tissue is applied, donors should be screened using NAT for HIV, HCV, and HBV. Serologically screened cardiovascular tissue carries a very low risk of HIV, HCV, or HBV transmission. Nevertheless, because effective virus inactivation is impossible (retention of tissue morphology) and the donor-recipient ratio may be as high as 1:10, we concluded that NAT should be performed for HIV, HCV, and HBV as an additional safety measure. Although cornea allografts carry the lowest risk of transmitting HIV, HCV, and HBV owing to corneal physiology, morphology, and the epidemiology of corneal diseases, NAT for HCV should still be performed. If the NAT screening of a donor for HIV, HCV, and HBV is negative, quarantine storage of the donor tissue seems dispensable. In view of numerous synergistic effects with transfusion medicine, it would be advantageous for tissue banks to cooperate with blood bank laboratories in performing virological tests.