We have identified an inexpensive, readily available, mechanically stable, extremely smooth, elastic, and mechanically uniform plastic suitable for thin film X-ray optics. Polyethylene terephthalate (PET) is easily deformed without losing its elastic properties or surface smoothness. Most important, PET can be coated with mono- or multilayers that reflect X-rays at grazing incidence. We have used these properties to produce X-ray optics made either as a concentric nest of cylinders or as a spiral. We have produced accurately formed shells in precisely machined vacuum mandresl or used a pin and wheel structure to form a continuously wound spiral. The wide range of medical, industrial and scientific applications for our technology includes: a monochromatic X-ray collimater for medical diagnostics, a relay optic to transport an X-ray beam from the target in a scanning electron microscop0e to a lithium-drifted silicon and microcalorimeter detectors and a satellite mounted telescope to collect celestial X-rays. A wide variety of mono- and multilayer coatings allow X-rays up to ~100 keV to be reflected. Our paper presents data from a variety of diagnostic measurements on the properties of the PET foil and imaging results form single- and multi-shell lenses.