Polarization, as one of the important properties of light, plays a very important role in the light field research and practical applications. The polarization measurement of the light field, especially the polarization distribution measurement of the light field with complex spatial structure, is an important subject to study the polarization characteristics of the light field and its application. Recently, as one of the main contents of the light field manipulation, the spatial modulation on the polarization state of light has become a hot topic. The spatial modulation for polarization of the light field constitutes a new class of laser beams with the characteristics of spatially varied polarization, also named vector beams. Owing to the unique properties of the spatially variant polarization and tight focusing, vector beams have received extensive attention in many scientific and engineering applications, such as femtosecond laser processing, super-resolution microscopy, optical micro-manipulation, and optical communication. Besides, the spatial modulation of polarization of the light field also enables spin-orbit interaction and polarization-related dynamic transmission behaviors, such as analogous optical activity in free space, polarization controlled Airy beam, spin selective imaging, etc. The propagation dynamics of the light field mainly depend on its polarization and phase distribution. Therefore, how to accurately and rapidly measure the polarization and phase distribution of the light field is a key problem in exploring new optical effects and enrich the related applications. On the other hand, as a carrier of light information, polarization plays an important role in the interaction between light and matter. By detecting the polarization information of the light field passing through the medium, the information about the composition and structure of the interacting materials can be obtained. Especially for the anisotropic materials, the polarization response can reveal the intrinsic structure and composition of materials, as well as the essential properties of scattering, emission and absorption. Therefore, measuring the polarization response of materials is of great significance for revealing the internal structure and birefringence property of materials, characterizing the complex modulation properties of optical devices, and exploring the physical mechanism of light-matter interaction. This review presents an overview of the recent advances of polarization measurement methods for the light field and optical anisotropy of materials. Firstly, the four representations of the polarization state of the light field are introduced, including polarization ellipse, Jones vector, Stokes parameters, and Poincaré sphere. Then, the measurement methods of Stokes parameters describing the polarization of the light fields and the Jones matrix of the anisotropic material are introduced, respectively. One of the measurement schemes for the Stokes parameters of the light fields is to record the intensity distributions at different detection states, where the most common one is the combination of a rotating retarder and a fixed analyzer. Due to time-sequential operation of rotating optical elements in the measurement process, it is unfavorable for fast measurement. The measurement speed can be improved by the multichannel simultaneous measurement. In this case, the amplitude of light field is divided into several channels, each of which is analyzed by suitable polarization optical elements. However, the measurement systems are complicated and cumbersome. With the development of micro-nano processing technology, the polarization measurement based on the metasurface can integrate the traditional polarization measurement system into a compact element, which can be further combined with a lens and image sensor to form full-Stokes polarization cameras. Another scheme for measuring Stokes parameters is based on the Pancharatnam-Berry (PB) phase theory and digital holography. It can not only greatly improve the measurement speed, but also obtain complete information of light fields, including the amplitude, phase, and polarization distributions in three-dimensional space. For the Jones matrix measurement of anisotropic materials, several measurement methods and their related applications based on digital holography are mainly introduced. From another point of view, the traditional intensity methods of polarization measurement are restricted to some specific application scenarios. These limits can be exceeded by introducing the well-designed metasurface elements, which cannot still measure the phase distribution. The polarization measurement method based on digital holography has the advantage of obtaining complete information of the light field, but it requires an interference optical path to provide a reference light beam. Therefore, we can choose different polarization measurement methods according to the practical application. Finally, for the Stokes parameters of light fields or the Jones matrix of materials, the development trend of polarization measurement technology is integration and rapidity.