In recent years, unmanned aerial vehicles (UAVs) have gained popularity due to their flexibility, mobility, and accessibility in various fields, including search and rescue (SAR) operations. The use of UAVs in SAR can greatly enhance the task success rates in reaching inaccessible or dangerous areas, performing challenging operations, and providing real-time monitoring and modeling of the situation. This article aims to help readers understand the latest progress and trends in this field by synthesizing and organizing papers related to UAV search and rescue. An introduction to the various types and components of UAVs and their importance in SAR operations is settled first. Additionally, we present a comprehensive review of sensor integrations in UAVs for SAR operations, highlighting their roles in target perception, localization, and identification. Furthermore, we elaborate on the various applications of UAVs in SAR, including on-site monitoring and modeling, perception and localization of targets, and SAR operations such as task assignment, path planning, and collision avoidance. We compare different approaches and methodologies used in different studies, assess the strengths and weaknesses of various approaches, and provide insights on addressing the research questions relating to specific UAV operations in SAR. Overall, this article presents a comprehensive overview of the significant role of UAVs in SAR operations. It emphasizes the vital contributions of drones in enhancing mission success rates, augmenting situational awareness, and facilitating efficient and effective SAR activities. Additionally, the article discusses potential avenues for enhancing the performance of UAVs in SAR.