Our work is built around the question of how model order reduction can be performed on hyperbolic, in particular wave-type, parametrized partial differential equations. The problem is that the convergence speed of linear model order reduction techniques cannot be better than the Kolmogorov N-width and that the Kolmogorov N-width of hyperbolic problems only decays slowly. This talk will address to what extent discontinuous Galerkin Trefftz formulations of parametrized partial differential equations and its associated Trefftz spaces are suitable for model order reduction techniques. Trefftz finite element formulations use trial and test functions that solve the corresponding PDE locally on each mesh element. In order to approximate the boundary conditions well, they cannot be continuous on the whole domain and therefore are discontinuous Galerkin methods by nature. We construct non-linear model order reduction techniques that build on dG Trefftz formulations. Our approaches are based on these formulations because, on the one hand, they are efficient and established finite element methods. On the other hand, as the basis functions of the Trefftz spaces depend on the parameter of the PPDE. This provides opportunities for the construction of non-linear reduction techniques that other finite element formulations do not offer. Every model order reduction approach can be represented by an encoder function, which reduces a function from a high-dimensional space to a low-dimensional vector, and a decoder function, which converts the low-dimensional vector back into the high-dimensional space. We discuss what the decoder and encoder functions of an efficient non-linear dG Trefftz model order reduction technique could look like and how to determine them, e.g., by using neural networks. The approaches are tested in numerical experiments. Although the work is still in its early stages, the results of the numerical experiments indicate that dG Trefftz methods have the potential to be well suited for efficient non-linear model order reduction techniques.