UPT quarter waveplates create a quarter-wavelength phase shift (π/2, 90°) and can convert linear polarization to circular polarization and vice versa. They are often used with a linear polarizer to form an isolator, blocking light reflected back from other surfaces (ellipsometry, optical pumping, isolation).
UPT half waveplates retard one polarization direction by half a wavelength (π, 180°), effectively changing the direction of linear polarization, depending on the orientation of incident linear polarization with respect to the crystal axis. Therefor they can be used as continuously adjustable polarization rotators e.g. in electro optical modulation or as a variable beam splitter when used in combination with a polarizing beam splitter.