Epoxides and aziridines are important building blocks for inhibitors of cysteine proteases which are promising drug targets for many diseases. In spite of the large amount of experimental data concerning inhibition potency, structure-activity relationships, and structural arrangements of enzyme-inhibitor complexes, little is known about the basic principles which connect the substitution pattern with the resulting activities. To shed some light on this issue which is essential for the rational design of improved compounds, we have studied the inhibition processes theoretically for various inhibitors using quantum mechanical/molecular mechanical hybrid approaches and classical molecular dynamics simulations. The careful analysis of the computational results allows insight into the interactions which govern the regio- and stereospecificity of the interactions. Known structure-activity relationships are rationalized in terms of the same interactions that determine the measured pH dependencies. Inconsistencies in existing X-ray structures are resolved through comparison with the computed structures, which leads to a reassessment of the factors that control the inhibition potency. Similarities and differences in the mode of action of epoxide- and aziridine-based inhibitors are elucidated. Finally the small reaction barriers computed for the irreversible step in E64 analogues call into question the commonly accepted two-step model of inhibition since the second, irreversible step is predicted to be so fast that suitably oriented enzyme-inhibitor complexes will react rather than dissociate and equilibrate.