Shear thickening polishing (STP) is an advanced surface finishing technology that leverages the unique properties of shear thickening fluid (STF) to achieve high-precision and high-efficiency polishing of complex surfaces. STF, which exhibits a dramatic increase in viscosity under applied shear stress, enables the polishing medium to adapt dynamically to the surface topography, ensuring uniform material removal and superior surface quality. This chapter reviews the fundamental principles of STP, including the rheological behavior of STF and the mechanisms of material removal during the polishing process. Key factors influencing the performance of STF, such as dispersion medium, temperature and type of abrasive particles, are discussed. The advantages of STP, such as its ability to handle freeform surfaces and reduce surface defects, are contrasted with traditional polishing methods. Finally, future research directions and potential advancements in STP technology are outlined, emphasizing its potential to revolutionize precision manufacturing processes.