Mammalian SWI/SNF complexes are ATP-dependent chromatin remodeling complexes that regulate genomic architecture. Here, we present a structural model of the endogenously purified human canonical BAF complex bound to the nucleosome, generated using cryoelectron microscopy (cryo-EM), cross-linking mass spectrometry, and homology modeling. BAF complexes bilaterally engage the nucleosome H2A/H2B acidic patch regions through the SMARCB1 C-terminal α-helix and the SMARCA4/2 C-terminal SnAc/post-SnAc regions, with disease-associated mutations in either causing attenuated chromatin remodeling activities. Further, we define changes in BAF complex architecture upon nucleosome engagement and compare the structural model of endogenous BAF to those of related SWI/SNF-family complexes. Finally, we assign and experimentally interrogate cancer-associated hot-spot mutations localizing within the endogenous human BAF complex, identifying those that disrupt BAF subunit-subunit and subunit-nucleosome interfaces in the nucleosome-bound conformation. Taken together, this integrative structural approach provides important biophysical foundations for understanding the mechanisms of BAF complex function in normal and disease states.