Accurate characterization and control of open quantum systems exposed to realistic, non-Markovian noise are vital for exploiting the full potential of quantum technologies and eventually reaching quantum fault tolerance. I will describe how to leverage the mathematical notion of a “frame” to build a simplified, “model-reduced” representation of the noisy dynamics of interest, which is directly tied to the available, finite control resources. Such a frame-based, “control-adapted” formulation overcomes important limitations of existing approaches. In particular, I will outline how it allows i) to implement quantum noise spectroscopy beyond the traditional frequency-domain setting, with emphasis on digital, time-domain characterization of non-stationary noise; and ii) to achieve noise-optimized quantum gate design, with emphasis on ongoing applications to non-Gaussian noise.