This paper investigates unmanned aerial vehicle (UAV)-aided backscatter communication (BackCom) networks, where the UAV is leveraged to help the backscatter device (BD) forward signals to the receiver. Based on the presence or absence of a direct link between BD and receiver, two protocols, namely transmit-backscatter (TB) protocol and transmit-backscatter-relay (TBR) protocol, are proposed to utilize the UAV to assist the BD. In particular, we formulate the system throughput maximization problems for the two protocols by jointly optimizing the time allocation, reflection coefficient and UAV trajectory. Different static/dynamic circuit power consumption models for the two protocols are analyzed. The resulting optimization problems are shown to be non-convex, which are challenging to solve. We first consider the dynamic circuit power consumption model, and decompose the original problems into three sub-problems, namely time allocation optimization with fixed UAV trajectory and reflection coefficient, reflection coefficient optimization with fixed UAV trajectory and time allocation, and UAV trajectory optimization with fixed reflection coefficient and time allocation. Then, an efficient iterative algorithm is proposed for both protocols by leveraging the block coordinate descent method and successive convex approximation (SCA) techniques. In addition, for the static circuit power consumption model, we obtain the optimal time allocation with a given reflection coefficient and UAV trajectory and the optimal reflection coefficient with low computational complexity by using the Lagrangian dual method. Simulation results show that the proposed protocols are able to achieve significant throughput gains over the compared benchmarks.