Decades of mutagenesis and clastogenesis studies have yielded enough structure-activity-relationship (SAR) information to make feasible the construction of computational models for prediction of endpoints based on molecular structure and reactivity. Although there is cause for optimism that these approaches might someday reduce or eliminate the need for actual genotoxicity testing, we are in fact a long way from this. We provide an overview of the state of the art of such approaches, dissecting out how these models are suboptimal. It is clear that current programs still have limited predictive capabilities. We propose that one of the major contributing factors for the inherent lack of sensitivity (typically 50-60%) is inadequate coverage of non-covalent DNA interactions. Suboptimal specificity can be partly attributed to chemical space considerations with associated non-causal activity correlations.