Ultracold fermions in optical lattices provide a clean physical realization of the celebrated Fermi-Hubbard model of condensed matter, a minimal model believed to contain the essential ingredients for high-temperature superconductivity. Recent advances in the field of quantum gas microscopy have opened up the possibility to probe and manipulate Fermi-Hubbard systems at the atomic level, enabling quantitative studies at temperatures that are challenging for state-of-the-art simulations on classical computers. In this talk I will report on experiments that probe equilibrium spin and density correlations in the Hubbard model in new regimes, including a repulsive spin-imbalanced system and a doped attractive system, which are related to each other through a mathematical mapping. I will also report on experiments where we measure the transport properties of doped repulsive systems. We find that the resistivity exhibits a linear temperature dependence and shows no evidence of saturation, two characteristic signatures of a bad metal.