In the largest E3 ligase subfamily, Cul3 binds a BTB domain, and an associated protein-interaction domain such as MATH recruits substrates for ubiquitination. Here, we present biochemical and structural analyses of the MATH-BTB protein, SPOP. We define a SPOP-binding consensus (SBC) and determine structures revealing recognition of SBCs from the phosphatase Puc, the transcriptional regulator Ci, and the chromatin component MacroH2A. We identify a dimeric SPOP-Cul3 assembly involving a conserved helical structure C-terminal of BTB domains, which we call "3-box" due to its facilitating Cul3 binding and its resemblance to F-/SOCS-boxes in other cullin-based E3s. Structural flexibility between the substrate-binding MATH and Cul3-binding BTB/3-box domains potentially allows a SPOP dimer to engage multiple SBCs found within a single substrate, such as Puc. These studies provide a molecular understanding of how MATH-BTB proteins recruit substrates to Cul3 and how their dimerization and conformational variability may facilitate avid interactions with diverse substrates.