The "dimer model" is the study of random perfect matchings (or "dimer covers") of a graph. More generally, "n-dimer covers" are multisets of edges so that every vertex of the graph is covered by exactly n edges (counted with multiplicity). I will discuss an interesting class of probability measures on n-dimer covers which are related to SL(n)-webs. For these measures, the partition function is given by a determinant, and one can obtain nice formulas for local edge statistics and correlations.