The additive manufacture of polymer optical elements has the promise of reducing component weight, providing new design capabilities, and enhanced performance for a wide variety of military and commercial optical systems. We review progress in the development of three-dimensional (3D)-printed gradient index (GRIN) lenses and optical phase masks. The 3D printing process uses a modified commercial inkjet printer and ultraviolet curable polymers that have specific nanoparticles added to them to modulate the index of refraction. Complex optical phase masks for the generation of Airy laser beams and polymer GRIN lenses to replace conventional glass lenses used in a telescope or riflescope are created. The generation and propagation of Airy beams using these polymer-generated optical phase masks have been investigated and analyzed through experimentation, simulations, and comparison with recent theoretical predictions. Airy beams have been generated using the conventional approach with a spatial light modulator and compared to the 3D printed optical phase masks. The maximum nondiffracting propagation distance of an aperture truncated Airy beam was experimentally measured. The results show that the maximum nondiffracting propagation distance of a laboratory generated Airy beam is proportional to x02, the Airy beam waist size squared. The size of the Gaussian envelope beam has a weaker effect on the Airy beam propagation distance. The experimental results were compared with current theoretical models. A set of 1-inch-diameter 100-mm focal length polymer GRIN lenses have been made using 3D printing. Transmission and modulation transfer function results for the lenses are reported.