Abstract: With the discoveries of novel materials, efforts are underway to create hybrid multilayers by stacking them together to form complex heterostructures and to explore new emergent fundamental physics governed by electron correlations. Experimental results on drag resistivity between quantum wires and double-layer graphene heterostructures triggered theoretical works, including new proposals for the mechanisms of this phenomenon. I am going to talk about the predictive theory of Coulomb drag and its relative phenomenon of near-field heat transfer in the context of correlated electron phases and investigate unexplored regimes of quantum transport in various mesoscale systems.