Recent advances in the design and recording of holographic optical elements are illustrated by means of two representative examples - focussing lens and multiple beam grating. The focussing lens design method is based on an analytic ray-tracing procedure that yields an analytic solution for the diffractive grating function. It will be elucidated by describing the recording and testing ofaspheric low 1 number focussing elements for 10. 6 microns wavelength having diffraction - limited performance over a broad range of incidence angles. The design of the multiple beam grating is based on solving a set of nonlinear equations to obtain a grating structure that can convert one incident beam into a set of specified output beams. Both the lens and the multiple grating elements are recorded with binary optics that involve computer generated plots with high resolution laser printer and plotolithographic techniques. Reflective and trismissive elements are formed by either etching reflective metal layers or GaAs substrates. 1.