A compressible Reynolds-Averaged Navier-Stokes solver was used to investigate the performance and flow physics of the cycloidal rotor (cyclocopter). This work employed a computational methodology to understand the complex aerodynamics of the cyclocopter and its relatively unexplored application for MAVs. The numerical code was compared against performance measurements obtained from experiment and was seen to exhibit reasonable accuracy. With validation of the flow solver, CFD predictions were used to gain qualitative insight into the flowfield. Time histories revealed large periodic variations in thrust and power. In particular, the virtual camber effect was found to significantly influence the vertical force time history. Spanwise thrust and flow visualizations showed a highly three-dimensional flowfield with large amounts of blade shedding and blade-vortex interaction. Overall, the current work seeks to provide unprecedented insight into the cyclocopter flowfield with the goal of developing an accurate predictive tool to refine the design of future cyclocopter configurations.