Here I will discuss the role of structural twisting and symmetry in determining the vibrational behaviors of non-symmorphic materials and how these translate into spectral features and functionalities. We advance a ‘twist’ dynamical description of quasiparticles (e.g., phonons, Bloch electrons) in chiral and achiral crystals. This twisting description provides a fresh perspective on symmetry-enforced crossings, quasiparticle interactions, scattering observables, and band topologies. L.L. acknowledges support from the U. S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division.