New techniques for studying the dynamics of Earth's plasmasphere and magnetosphere from space are at hand. Global images of these regions can be obtained by remote sensors which detect two types of emissions: extreme ultraviolet (EUV) photons and energetic neutral atoms (ENA). Efficient imagers for EUV and ENA share several important features, including a wide field of view, high throughput, the absence of transmitting optics, appropriate time and spatial resolution, and similar detectors. We have built and tested prototypes of imagers whose designs recognize these common requirements. Coded apertures replace lenses to provide the needed spatial resolution. A special class of aperture designs permits artifact-free reconstruction (limited only by noise) of any source region within the field of view, even if the source overfills the field of view. These designs also provide signal to noise ratios superior to those of a single-aperture imager in most applications contemplated here. We have evaluated thin-film filters to block the H Ly α flux that interferes with ENA measurements, and we rely on coincidence requirements to further reduce interference. We consider alternative techniques, including a reflective optics imager for EUV that uses special multilayer coatings we have designed, and a version of the ENA imager that uses a solid-state detector.