Research progress on terahertz achromatic broadband polarization wave plates

•Using the number of structural layers as a main basis, develop an in-depth classification of wave plate types based on material and design structure.•The pros and drawbacks of various wave plates and bandwidth materials are clearly contrasted in the form of the tables.•The current state of the terahertz achromatic wideband wave plates is outlined, as are the major ideas for designing a wideband dispersion-engineering wave plate.•The significance of metamaterials in the design of terahertz wave plates is discussed, as well as the prospects for future development.