Mammalian SWI/SNF (mSWI/SNF) adenosine triphosphate-dependent chromatin remodelers modulate genomic architecture and gene expression and are frequently mutated in disease. However, the specific chromatin features that govern their nucleosome binding and remodeling activities remain unknown. We subjected endogenously purified mSWI/SNF complexes and their constituent assembly modules to a diverse library of DNA-barcoded mononucleosomes, performing more than 25,000 binding and remodeling measurements. Here, we define histone modification-, variant-, and mutation-specific effects, alone and in combination, on mSWI/SNF activities and chromatin interactions. Further, we identify the combinatorial contributions of complex module components, reader domains, and nucleosome engagement properties to the localization of complexes to selectively permissive chromatin states. These findings uncover principles that shape the genomic binding and activity of a major chromatin remodeler complex family.