The strong coupling of electromagnetic radiation to a phonon in a material results in the formation of a phonon polariton. In highly anisotropic hyperbolic materials, the hyperboloid shape of the isofrequency contour enables phonon polaritons to have unbounded k vectors and therefore unbounded momentum in the ideal limit, giving them unique applications in nanophotonic devices. In this Maple worksheet, we will first explore the  physics behind hyperbolic materials and the high-momentum hyperbolic phonon polaritons they support. We will then discuss the numerous applications of hyperbolic phonon polaritons, from subdiffraction limit imaging to optical sensing. Lastly, we will end with a discussion of materials which are known to form hyperbolic phonon polaritons. Application uses the Maple Quantum Chemistry Toolbox.