Tandem repeats (TRs) are abundant in proteomes across all kingdoms of life. Having an impressive variety of sizes, structures and functions, TRs often offer enhanced binding properties and are associated with disease and immunity related functions. While mechanisms generating protein TRs are poorly understood, natural selection contributes to shaping their evolution, and TR expansion may be linked to the origin of novel genes.Specific combinations of TR units with point mutations/indels are able to ensure desirable protein properties.Indeed, the design-ability of domain TRs has been successfully exploited in bioengineering. However, the experimental search for optimal TR configurations is difficult/inefficient due to the huge number of possible combinations. We will address this by modeling the evolution and natural selection in naturally observed proteins with domain TRs. Combined with annotations of structure, function and protein-protein interactions, we will pinpoint the naturally occuring evolutionary innovations, i.e., TR configurations that have been fixed by selection due to adaptive benefits. These predictions can serve as testable hypotheses in protein engineering experiments, allowing to narrow down the search to combinations with optimal properties according to the natural evolution history. For ankyrin and armadillo repeats, employed to design medically relevant proteins, specific recommendations will be made for further experimental testing.