Biological sequences in evolutionary trajectories of are propelled by mutation and whittled away by selection to maintain function. Present-day sequences can therefore be regarded as the outcomes of millions of evolutionary experiments that record functional constraints in the genotype-phenotype map. In this talk we will introduce computational methods that, when combined with recent growth in sequence databases, quantify evolutionary constraints in terms of evolutionary couplings between residues. We have applied these tools to predict (i) accurate 3D structures of proteins, RNA and complexes, (ii) conformational order and plasticity in ‘disordered’ proteins and (iii) quantitative effects of mutations on organism fitness. These computational approaches address the challenge of inferring causality from correlations in genetic sequences but can be applied more widely to other biological information such as gene expression or dynamics, cellular phenotypes or drug response.