The emergence of high-throughput technologies for measuring biological systems has introduced problems for data interpretation that must be addressed for proper inference. First, analysis techniques need to be matched to the biological system, reflecting in their mathematical structure the underlying behavior being studied. When this is not done, mathematical techniques will generate answers, but the values and reliability estimates may not accurately reflect the biology. Second, analysis approaches must address the vast excess in variables measured (e.g. transcript levels of genes) over the number of samples (e.g. tumors, time points), known as the large-p, small-n problem. In large-p, small-n paradigms, standard statistical techniques generally fail, and computational learning algorithms are prone to overfit the data. Here we review the emergence of techniques that match mathematical structure to the biology, the use of integrated data and prior knowledge to guide statistical analysis, and the recent emergence of analysis approaches utilizing simple biological models. We show that novel biological insights have been gained using these techniques.