Waste fiber-reinforced plastics (FRP) and unsaturated polyesters were readily depolymerized by subjecting them to a treatment with ionic liquids under heating conditions. The use of microwaves for heating effectively progressed depolymerization, whereas the conventional heating method was ineffective for this purpose. We isolated the monomeric material, phthalic anhydride, by direct distillation from the reaction pot under reduced pressure with yields of more than 90 %. We recovered the glass fibers in a pure form and achieved the effective removal of polystyrene, the linker unit of FRP. Ionic liquids were useful for several iterations of the reaction, and purification of the used ionic liquids was also possible. Thus, we developed a new use of ionic liquids for chemical recycling of waste plastics.