Dimer models are of interest from many perspectives across geometry, combinatorics, and mathematical physics. In this talk, we explain how one throughline among these perspectives --- the spectral relationship between dimer models in T^2 and line bundles on curves in (C*)^2 --- may be understood as part of a more general mirror relationship between simplicial complexes in T^n and coherent sheaves on (C*)^n. We refer to the complexes arising this way as tropical Lagrangian coamoebae, as from a symplectic point of view they are in a sense dual objects to tropical varieties. This is joint work with Chris Kuo.