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To stimulate interaction and collaboration across scientific fields, we introduce a minimum set of biological criteria that theoretical models of aging should satisfy. We review results of several recent experiments that examined changes in age-specific mortality rates caused by genetic and environmental manipulation. The empirical data from these experiments is then used to test mathematical models of aging from several different disciplines, including molecular biology, reliability theory, physics, and evolutionary biology/population genetics. We find that none of the current models are consistent with all of the published experimental findings. To provide an example of how our criteria might be applied in practice, we develop a new conceptual model of aging that is consistent with our observations.