Capabilities of the Three-dimensional Euler Aerodynamic Method (TEAM) for simulating nonlinear aerodynamics associated with transonic flows and leading-edge vortex flows are assessed. TEAM is based on a cell-centered finite-volume, multistage time-stepping algorithm. It accommodates patched zonal grids of arbitrary topologies with matched as well as mismatched grid distributions at the interfaces. Its ability to handle complex geometries, robustness, accuracy, and parametric sensitivity are used as the assessment criteria. Sensitivity of solutions to three numerical dissipation schemes and grid-density variations is investigated. Transonic-flow solutions for NLR 7301 airfoil, Wing C, and a canard-wing-body, and low-speed leading-edge vortex-flow solutions for a delta wing, a cropped-delta wing, and a double-delta wing-body are presented. The solutions are correlated with experimental data and other numerical solutions as applicable. The results provide a good measure of TEAM's capabilities.