Positron annihilation spectroscopy for chemical analysis (PASCA) has been developed to analyze the microstructure of polymers. Positron annihilation lifetime measurements give direct information about the dimension and contents of free-volume holes in amorphous materials. The angular correlation measurements of positron annihilation radiation give additional information about the shape of the free-volume holes in oriented polymeric materials. The unique capability of PASCA to probe free-volume properties is from the fact that positronium atom is trapped in the atomic-scale holes which have a size ranging from 1 to 10 Å. Theoretical aspects, experimental developments of PASCA, and examples in analyzing the microstructures of epoxy, PEEK, and PMMA polymers are presented