The sequencing of the human genome heralded the new age of ‘genetic medicine’ and raised the hope of precision medicine facilitating prolonged and healthy lives. Recent studies have dampened this expectation, as the relationships among mutations (termed ‘risk factors’), biological processes, and diseases have emerged to be more complex than initially anticipated. In this review, we elaborate upon the nature of the relationship between genotype and phenotype, between chance-laden molecular complexity and the evolution of complex traits, and the relevance of this relationship to precision medicine. Molecular contingency, i.e., chance-driven molecular changes, in conjunction with the blind nature of evolutionary processes, creates genetic redundancy or multiple molecular pathways to the same phenotype; as time goes on, these pathways become more complex, interconnected, and hierarchically integrated. Based on the proposition that gene-gene interactions provide the major source of variation for evolutionary change, we present a theory of molecular complexity and posit that it consists of two parts, necessary and unnecessary complexity, both of which are inseparable and increase over time. We argue that, unlike necessary complexity, comprising all aspects of the organism’s genetic program, unnecessary complexity is evolutionary baggage: the result of molecular constraints, historical circumstances, and the blind nature of evolutionary forces. In the short term, unnecessary complexity can give rise to similar risk factors with different genetic backgrounds; in the long term, genes become functionally interconnected and integrated, directly or indirectly, affecting multiple traits simultaneously. We reason that in addition to personal genomics and precision medicine, unnecessary complexity has consequences in evolutionary biology.