Chiroptics is the study of the changes in circular polarization states of light transmitted through analytes typically dissolved in isotropic solutions. However, experimental challenges have long prevented chiroptical measurements of anisotropic media such as single crystals of low symmetry, liquid crystals, or structured films. The high accuracy universal polarimeter (HAUP) was introduced in 1983 to investigate the differential refraction of left and right circular polarization states, circular birefringence (CB), and even in anisotropic media that are dominated by the differential refraction of orthogonal linear polarization states, linear birefringence (LB). In this century, the HAUP was extended to also measure not only the dispersive optical effects (CB and LB) but also the corresponding dissipative effects, circular dichroism (CD) and linear dichroism (LD), differences in light absorption. The improved device is the generalized-HAUP (G-HAUP). Not only can it deliver all the linear optical properties of dissymmetric, anisotropic, and absorbing media, but it can also do so in the ultraviolet as well as the visible part of the electromagnetic spectrum. In this review, characteristic features of the G-HAUP and its applications to crystals of photomechanical salicylidenephenylethylamines, alanine, benzil, and magneto-optical CeF3 are described.