Cyclin-dependent kinases (CDKs) are activated upon cyclin-binding to enable progression through the cell cycle. Dominant CDKs and cyclins in mammalian cells include CDK1, CDK2, CDK4, and CDK6 and corresponding cyclins A, B, D, and E. While only certain, "typical" cyclin/CDK complexes are primarily responsible for cell cycle progression, "atypical" cyclin/CDK complexes can form and sometimes perform the same roles as typical complexes. We asked what structural features of cyclins and CDKs favor the formation of typical complexes, a vital yet not fully explored question. We use computational docking and biophysical analyses to exhaustively evaluate the structure and stability of all CDK and cyclin complexes listed above. We find that binding of the complexes is generally stronger for typical than for atypical complexes, especially when the CDK is in an active conformation. Typical complexes have denser clusters, indicating that they have more defined cyclin-binding sites than atypical complexes. Our results help explain three notable features of cyclin/CDK function in the cell cycle: (i) why CDK4 and cyclin-D have exceptionally high specificity for each other; (ii) why both cyclin-A and cyclin-B strongly activate CDK1, whereas CDK2 is only strongly activated by cyclin-A; and (iii) why cyclin-E normally activates CDK2 but not CDK1. Overall, this work reveals the binding modalities of cyclin/CDK complexes, how the modalities lead to the preference for typical complexes versus atypical complexes, and how binding modalities differ between typical complexes. Our observations suggest targeting CDK catalytic actions through destabilizing their native differential cyclin interfaces.