Abstract: New quantum simulation platforms provide an unprecedented microscopic perspective on the structure of strongly correlated quantum matter. This allows to revisit decade-old problems from a fresh perspective, such as the two-dimensional Fermi-Hubbard model, believed to describe the physics underlying high-temperature superconductivity. In order to fully use the experimental as well as numerical capabilities available today, we need to go beyond conventional observables, such as one- and two-point correlation functions. In this talk, I will give an overview of recent results on the Hubbard model obtained through novel analysis tools: using machine learning techniques to analyze quantum gas microscopy data allows us to take into account all available information without a potential bias by the choice of an observable and compare different theories on a microscopic level. I will introduce a novel, customized neural network architecture, which features full interpretability and thus enables direct physical insights. The analysis of data from quantum simulation experiments of the doped Fermi-Hubbard model with machine learning tools as well as through different higher-order correlations shows a qualitative change in behavior around 20% doping, consistent with condensed matter experiments on cuprate materials. As an outlook, I will discuss how our microscopic understanding of the low doping limit has led us to the discovery of a binding mechanism, which enables pairing of charge carriers at currently accessible experimental temperatures, thus paving the way for the study of pair formation in cold atom quantum simulators.