Object detection and tracking are essential for surveillance, navigation, and Search and Rescue (SAR) operations. The maritime environment presents unique challenges, including low visibility, sea clutter, dense fog, and dynamic backgrounds. These factors significantly hinder manual detection and tracking during both daytime and nighttime operations. Therefore, efficient and automated detection and tracking systems are critically required. This paper presents a systematic survey of recent advancements in real-time object detection and tracking techniques, with a primary focus on their application in maritime SAR missions using unmanned aerial vehicles (UAVs). The study categorizes and compares classical approaches and modern deep learning-based models, including their integration with visual and infrared (IR) imagery. Particular attention is given to performance characteristics, computational complexity, and deployment feasibility on resource-constrained UAV platforms. The survey identifies key limitations of current detection and tracking methods under challenging maritime conditions and highlights open research challenges. Finally, future research directions are outlined to optimize real-time UAV-based maritime SAR operations.