The unmanned aerial vehicle (UAV) offers inherent mobility and advanced communication capabilities, making it suitable for agile deployment and adaptable observation compared to traditional fixed sensing systems. In various sensing applications, particularly those requiring low transmission delays, multiple distributed tasks must be efficiently managed. Optimizing the mission completion time in such delay-constrained multi-task UAV-based sensing scenarios necessitates careful design of inter-task trajectories, UAV-base station (BS) associations, and sensing sequences. However, achieving an optimal sensing scheme is challenging due to the interdependencies and non-convex constraints involved in these sub-problems. To address these challenges, this chapter introduces a space pruning-based trajectory search (SPTS) algorithm that leverages geometric properties to expedite the convergence compared to conventional methods like the Ployblock algorithm. Secondly, an optimal UAV-BS association algorithm is developed to efficiently determine the optimal BS for each sensing task. Finally, integrating these algorithms with the Lin-Kernighan-Helsgaun (LKH) algorithm enables computation of a lower bound for mission completion time and derivation of near-optimal solutions. Numerical simulations validate the effectiveness of the proposed approach, demonstrating significant performance enhancements in UAV-based sensing applications.