For nearly 60 years, significant research efforts have been focused on developing strategies for the cycloaddition of bicyclobutanes (BCBs). However, higher-order cycloaddition and catalytic asymmetric cycloaddition of BCBs have been long-standing formidable challenges. Here, we report Pd-catalyzed ligand-controlled, tunable cycloadditions for the divergent synthesis of bridged bicyclic frameworks. The dppb ligand facilitates the formal (5+3) cycloaddition of BCBs and vinyl oxiranes, yielding valuable eight-membered ethers with bridged bicyclic scaffolds in 100% regioselectivity. The Cy-DPEphos ligand promotes selective hetero-[2σ+2σ] cycloadditions to access pharmacologically important 2-oxabicyclo[3.1.1]heptane (O-BCHeps). Furthermore, the corresponding catalytic asymmetric synthesis of O-BCHeps with 94-99% ee has been achieved using chiral (S)-DTBM-Segphos, representing the first catalytic asymmetric cross-dimerization of two strained rings. The obtained O-BCHeps are promising bioisosteres for ortho-substituted benzenes.