This review covers literature between 2003-2021The development and application of genome mining tools has given rise to ever-growing genetic and chemical databases and propelled natural products research into the modern age of Big Data. Likewise, an explosion of evolutionary studies has unveiled genetic patterns of natural products biosynthesis and function that support Darwin's theory of natural selection and other theories of adaptation and diversification. In this review, we aim to highlight how Big Data and evolutionary thinking converge in the study of natural products, and how this has led to an emerging sub-discipline of evolutionary genome mining of natural products. First, we outline general principles to best utilize Big Data in natural products research, addressing key considerations needed to provide evolutionary context. We then highlight successful examples where Big Data and evolutionary analyses have been combined to provide bioinformatic resources and tools for the discovery of novel natural products and their biosynthetic enzymes. Rather than an exhaustive list of evolution-driven discoveries, we highlight examples where Big Data and evolutionary thinking have been embraced for the evolutionary genome mining of natural products. After reviewing the nascent history of this sub-discipline, we discuss the challenges and opportunities of genomic and metabolomic tools with evolutionary foundations and/or implications and provide a future outlook for this emerging and exciting field of natural product research.