Holographic optical elements (HOEs) can be used in systems and methods for providing illumination and for projecting images. The HOEs may be switchable HOEs, whose diffractive properties can be controlled. Described herein is a method of combining light from two or more illumination sources. In one embodiment, a reflection-type HOE is illuminated by the first illumination source. The HOE diffracts light from the first illumination source into an output direction. Light from the second illumination source is transmitted through the HOE and onto a reflective optical element, which reflects the light back through the HOE and into the same output direction. Also described is a projection system that uses two or more HOEs to combine two or more colors of light for use by a single image display. The system includes one or more light sources, an image display (such as a reflective or transmissive LCD display or a MEMS display, for example), and a first and a second HOE. The HOEs are each mounted between a light source and the image display, and configured to provide one color of light to the image display and from the image display into an output direction. In one embodiment, the HOEs are switchable HOEs and can be used for color-sequential display and/or for color balancing.