Abstract: While high-order harmonic generation is an efficient method for producing extreme ultraviolet (EUV) pulses from near-infrared ultrafast laser sources, it is very difficult to manipulate the polarization and spatial mode properties of the beams with EUV optics. However, controlling the source beam can make this possible. Selection rules for spin and angular momentum conservation play an important role to determine what is possible. In this talk we describe several methods that we have developed to generate harmonic beams with circular polarization and controllable orbital angular momentum. We will also describe how Hermite-Gauss input beams can generate arrays of harmonic beamlets that can be used for single-shot ptychographic imaging. All of these approaches use passive input beam transformations that are much more stable than methods that require beam splitting.