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Since the early days of the quantum theory of solids, the interaction between electrons and lattice vibrations has provided a long list of exciting discoveries. Examples include the role played by electron-phonon (e-ph) interaction in the development of the theory of superconductivity and conducting polymers, where charge doping is used to circumvent the Peierls transition. In the last decade, the theoretical prediction and observation of phonons with intrinsic chirality in two-dimensional materials brought a new ingredient to this long standing problem. In this talk I will provide an overview on this field and present our recent results on the effects of the interaction between electrons and chiral phonons in two-dimensional materials [1,2]. By using a non-perturbative solution we show that chiral phonons introduce inelastic Umklapp processes resulting in copropagating edge states which coexist with a continuum. Our results hint on the possibility of having new electron-phonon states of matter.