Advances in our capability to find patterns and their dynamics in turbulent fluid flows will improve our ability to predict, sense, control, and understand a range of systems relevant to science and engineering. However, modeling these systems is challenging due to the high-dimensional, chaotic, and multi-scale nature of turbulence. Fortunately, the construction of low-order representations of turbulence is being increasingly enabled by the progress in physics-based and data-driven modeling methods. Physics-based techniques, such as resolvent analysis, provide valuable insight about the underlying physical mechanisms sustaining turbulence, while data-driven methods, such as the spectral proper orthogonal decomposition (SPOD), identify statistically relevant flow features. Furthermore, recent hybrid approaches promise to enable physics learning from data. This symposium will bring together recent research efforts on the development of low-order models of turbulence and their application to pressing challenges in aeronautics, urban infrastructure, biomedicine and energy conversion.