This article investigates the distributed adaptive finite-time containment control problem for multi-UAVs with input constraints, actuator failures, communication limitations, and external disturbances. First, a new smoothing function is used to smooth the asymmetric input constraint signals so that the input constraint and actuator fault control problem can be transformed into a variable gain control problem. Subsequently, a new Nussbaum function is proposed to solve the variable gain control problem. A new adaptive event-triggered strategy is designed to solve the communication limitation problem, and the trigger threshold has the characteristic of adaptive adjustment that can be dynamically decreased. In response to external disturbances, an adaptive law is designed to estimate and compensate for the boundaries of disturbances. It follows from the analysis based on Lyapunov theory that under the proposed controller, the followers will converge to the convex envelope formed by the leaders in a finite time, and Zeno-free is achieved. Simulation results are provided to verify the effectiveness of the developed adaptive event-triggered finite-time fault-tolerant containment control laws.