Abstract: The Friedrichs' framework, originally introduced by Friedrichs in 1958, generalizes a large class of linear differential operators into an abstract setting. Examples of Friedrichs' operators include advection-reaction or convection-diffusion equations, the time-harmonic Maxwell equations or compressible linear elasticity. In recent years, the unified analysis and discretization of these operators has seen increased interest, in particular due to a well-founded variational theory that as been developed by now. In this talk we will explore the benefits of the framework for the fields of model order reduction (MOR) and for spectral multiscale approaches leveraging localized training. In a first step, we present a result that allows for the identification of exponentially approximable parametrized Friedrichs' systems (in the sense of Kolmogorov). This also generalizes established approximation-theoretic results to the case of parameter-dependent ansatz or test spaces which naturally occur in the variational formulations. Moreover, a least squares approach which is based on an ultraweak formulation and only requires minimal regularity is presented and subsequently used for the computation of reduced basis functions. In a second step, the by now well-established construction of local approximation spaces via localized training will be analyzed for Friedrichs' systems. For given subdomains, this procedure solves the underlying equation on an oversampling domain using randomized boundary data, restricts to the inner domain and finally compresses the resulting local solutions. Leveraging our theory, we will give a criterion when this method can be expected to work well.