Quasiparticle physics underlies our understanding of the microscopic dynamical behaviors of materials that govern a vast array of properties, including structural stability, excited states and interactions, dynamical structure factors, and electron and phonon conductivities. Thus, understanding band structures and quasiparticle interactions is foundational to the study of condensed matter. Here we advance a ‘twist’ dynamical description of quasiparticles (including phonons and Bloch electrons) in non-symmorphic chiral and achiral materials. Such materials often have structural complexity, strong thermal resistance, and efficient thermoelectric performance for waste heat capture and clean refrigeration technologies. The twist dynamics presented here provides a novel perspective of quasiparticle behaviors in such complex materials, in particular highlighting how non-symmorphic symmetries determine band crossings and anti-crossings, topological behaviors, quasiparticle interactions that govern transport, and observables in scattering experiments. We provide specific context via neutron scattering measurements and first-principles calculations of phonons and electrons in chiral tellurium dioxide. Building twist symmetries into the quasiparticle dynamics of non-symmorphic materials offers intuition into quasiparticle behaviors, materials properties, and guides improved experimental designs to probe them. More specifically, insights into the phonon and electron quasiparticle physics presented here will enable materials design strategies to control interactions and transport for enhanced thermoelectric and thermal management applications.