Studying quantum entanglement over the past 1--2 decades has allowed us to make remarkable theoretical progress in understanding correlated many-body quantum systems. However electrons in real materials experience random heterogeneities ("dirt") whose theoretical treatment, including strong correlations, has been a challenge. I will describe how synthesizing ideas from quantum information theory, statistical mechanics, and quantum field theory gives us new insights into the role of randomness in 2D correlated quantum spin systems. First I will outline our results on weak bond-randomness in two theoretically controlled cases ("valence-bond-solids" and classical dimer models) and apply them to random quantum magnets to show that topological defects with free spins necessarily nucleate and control the low energy physics. Second I will describe how the results lead us to conjectures, and a proof in 1D, of general entanglement-based constraints ("LSM theorems") on all possible low-energy fates of quantum magnets, that hold even with randomness. Third I will describe how the theory predicts a scaling collapse of the temperature and magnetic-field dependence of thermodynamic quantities that is consistent with experimental observations from multiple materials, suggesting that these materials exhibit randomness-driven long range entanglement.