This dissertation investigates the optimal aerodynamic performance and design of conventional and coaxial helicopters in hover and forward flight using conventional and higher harmonic blade pitch control. First, we describe a method for determining the blade geometry, azimuthal blade pitch inputs, optimal shaft angle rotor angle of attack, and division of propulsive and lifting forces among the components that minimize the total power for a given forward flight condition. The optimal design problem is cast as a variational statement that is discretized using a vortex lattice wake to model inviscid forces, combined with two-dimensional drag polars to model profile losses. The resulting nonlinear constrained optimization problem is solved via Newton iteration. We investigate the optimal design of a compound vehicle in forward flight comprised of a coaxial rotor system, a propeller, and optionally, a fixed wing. We show that higher harmonic control substantially reduces required power, and that both rotor and propeller efficiencies play an important role in determining the optimal shaft angle, which in turn effects the optimal design of each component. Second, we present a variational approach for determining the optimal minimum power torque-balanced coaxial hovering rotor using Blade Element Momentum Theory including swirl. We show that the optimal hovering coaxial rotor generates only a small percentage of its total thrust on the portion of the lower rotor operating in the upper rotors contracted wake, resulting in an optimal design with very different upper and lower rotor twist and chord distributions. We also show that the swirl component of induced velocity has a relatively small effect on rotor performance at the disk loadings typical of helicopter rotors. Third, we describe a more refined model of the wake of a hovering conventional or coaxial rotor.