In this chapter, we explore a UAV-assisted multi-user wireless power transfer (WPT) network, where a UAV is deployed to wirelessly transfer energy to multiple ground devices (GDs) distributed across a defined region. Our focus is on optimizing the UAV trajectory under maximum flying speed constraints to maximize the minimum energy harvested by the GDs over a defined charging duration. Unlike prior works that employed simplified linear energy harvesting (EH) models, this study introduces a realistic nonlinear EH model to address UAV trajectory design, marking its first application in this context. The formulated trajectory design problem is highly non-convex, involving infinitely many variables, which poses significant challenges for achieving an optimal solution. To address this, we propose a systematic three-step approach to derive an efficient solution. First, we rigorously characterize the optimal trajectory, which adopts a successive-hover-and-fly (SHF) structure, where the UAV hovers at designated points for efficient energy transfer and moves at maximum speed along arcs between these points. Leveraging this SHF structure, we reformulate the original problem to identify turning points that allow the UAV to change direction during maximum-speed flight without additional hovering. Finally, convex approximation techniques are employed to solve the reformulated problem. By utilizing the convex properties of the nonlinear EH model, an iterative approach is applied to solve a series of convex optimization problems, progressively refining the UAV trajectory towards a high-quality solution. Numerical results confirm the convergence of the proposed approach and substantiate its performance advantages over the benchmarks.