Abstract: We will introduce two-dimensional Dirac operators with delta-shell interactions, which are supported on a smooth unbounded curve that is straight outside a compact set, as well-defined self-adjoint operators. We will find their essential spectra and we will prove in different situations the existence of geometrically induced discrete eigenvalues. The talk is based on the preprint with J. Behrndt, P. Exner, and M. Holzmann, arXiv:2312.00181.