Over the past few decades, metasurfaces have revolutionized conventional bulky optics by providing an effective approach to manipulate optical waves at the subwavelength scale. This advancement holds great potential for compact, multifunctional, and reconfigurable optical devices. Notably, metasurfaces constructed with anisotropic nanostructures have exhibited remarkable capability in manipulating the polarization state of optical waves. Furthermore, they can be employed to achieve independent control of the amplitude and phase of optical waves in different polarization channels. This capability has garnered significant attention from the photonics community due to its unprecedented potential for polarization-selective and -multiplexed optical wave manipulation, offering versatile applications in optical imaging, communication, and detection. This paper reviews the design principles, representative works, and recent advancements in anisotropic nanostructures for optical polarization manipulation, detection, as well as polarization-selective and -multiplexed optical wave manipulation. Personal insights into further developments in this research area are provided.