The landscape of genomics has changed drastically in the last two decades. Increasingly inexpensive sequencing has shifted the primary focus from the acquisition of biological sequences to the study of biological function. Assays have been developed to study many intricacies of biological systems, and publicly available databases have given rise to integrative analyses that combine information from many sources to draw complex conclusions. Such research was the focus of the recent workshop at the Isaac Newton Institute, 'High dimensional statistics in biology'. Many computational methods from modern genomics and related disciplines were presented and discussed. Using, as much as possible, the material from these talks, we give an overview of modern genomics: from the essential assays that make data-generation possible, to the statistical methods that yield meaningful inference. We point to current analytical challenges, where novel methods, or novel applications of extant methods, are presently needed.