Enhancers regulate gene expression through the binding of sequence-specific transcription factors (TFs) to cognate motifs. Various features influence TF binding and enhancer function-including the chromatin state of the genomic locus, the affinities of the binding site, the activity of the bound TFs, and interactions among TFs. However, the precise nature and relative contributions of these features remain unclear. Here, we used massively parallel reporter assays (MPRAs) involving 32,115 natural and synthetic enhancers, together with high-throughput in vivo binding assays, to systematically dissect the contribution of each of these features to the binding and activity of genomic regulatory elements that contain motifs for PPARγ, a TF that serves as a key regulator of adipogenesis. We show that distinct sets of features govern PPARγ binding vs. enhancer activity. PPARγ binding is largely governed by the affinity of the specific motif site and higher-order features of the larger genomic locus, such as chromatin accessibility. In contrast, the enhancer activity of PPARγ binding sites depends on varying contributions from dozens of TFs in the immediate vicinity, including interactions between combinations of these TFs. Different pairs of motifs follow different interaction rules, including subadditive, additive, and superadditive interactions among specific classes of TFs, with both spatially constrained and flexible grammars. Our results provide a paradigm for the systematic characterization of the genomic features underlying regulatory elements, applicable to the design of synthetic regulatory elements or the interpretation of human genetic variation.