Transport in strongly correlated materials is one of the central topics in condensed matter physics. Due to major prospects for technological applications, particular attention is paid to the cuprate superconductors, and by association, to kappa-organic materials and moiré systems. The last decade has seen great progress in the understanding of the generic high-temperature properties of these systems, largely based on the microscopic yet simplified interacting lattice models. However, there are multiple outstanding questions regarding their low-temperature physics. The mechanism of the strange-metallic linear-in-temperature resistivity and its relation to superconductivity have so far eluded understanding. There is conflicting evidence for the quantum critical (QC) scenario, which is a common view that there is a zero-temperature QC point hidden behind the superconducting dome on the phase diagram of the cuprates. Recent magnetoresistance measurements in these and other materials contribute to a puzzling phenomenology. The factors that determine the magnitude of the superconducting critical temperature are also poorly understood. Further progress is blocked by the limitations of quantum many-body numerical methods. To address these questions, we propose to employ a highly promising new approach to the numerical solution of the many-electron problem. It may overcome the long-standing limitations and allow for an unprecedented accuracy and control. The real-frequency diagrammatic Monte Carlo method will yield numerically exact results for the resistivity in a range of lattice models, at low temperature, and as a function of magnetic field. These results will help interpret recent experimental results, set new predictions, and open doors to reverse-engineering of functional materials. The tools we develop will be readily applicable to a wide range of condensed matter physics problems, and we will make all code packages publicly available.