The development of Structural Health Monitoring (SHM) and Non-Destructive Testing (NDT) techniques has rapidly evolved and matured over the past few decades. Advances in sensor technology have facilitated deploying SHM systems for large-scale structures and local NDT of structural members. Although both methods have been successfully applied to identify structural damage in various systems, Environmental and Operational Condition (EOC) variations can influence sensor measurements and mask damage signatures in the structural response. EOCs include environmental conditions, such as temperature, humidity, and wind, as well as operational conditions, such as mass loading, vibration, and boundary conditions. The effect of EOCs can significantly undermine the reliability and robustness of damage assessment technologies and limit their performance. Thus, successful SHM and NDT systems can compensate for changing EOCs. This paper provides a state-of-the-art review of the effects of EOCs on SHM and NDT systems. It presents recent developments in advanced sensing technology, signal processing, and analysis techniques that aim to eliminate the masking effect of EOC variations and increase the damage sensitivity and performance of SHM and NDT systems. The paper concludes with current research challenges, trends, and recommendations for future research directions.