One of the major challenges facing the analysis of high-throughput microarray measurements is how to extract in a systematic and rigorous way the biologically relevant components from the experiments in order to establish meaningful connections linking genetic information to cellular function. Because of the significant amount of experimental information that is generated (expression levels of thousands of genes), computer-assisted knowledge extraction is the only realistic alternative for managing such an information deluge. Mathematical programming offers an interesting alternative for the development of systematic methodologies aiming toward such an analysis. We summarize recent developments related to critical problems in the analysis of microarray data; namely, tissue clustering and classification, informative gene selection, and reverse engineering of gene regulatory networks. We demonstrate how advances in nonlinear and mixed-integer optimization provide the foundations for the rational identification of critical features unraveling fundamental elements of the underlying biology thus enabling the interpretation of volumes of biological data. We conclude the discussion by identifying a number of related research challenges and opportunities for further research.