There is a bijective correspondence between random domino tilings on a Temperleyan polyomino and random spanning trees on its dual graph.  These wired uniform spanning trees (WUSTs) can be algorithmically constructed through loop-erased random walks (LERWs) on the square grid, the distributional limit of which is observed to be Schramm-Loewner evolutions (SLEs) on a bounded complex domain.  In this talk, we will define these objects and discuss the connections between them, which broadly suggest a deep connection between SLEs and random domino tilings.