One of the main goals of molecular biology is to understand the structure of biomolecules. With the emergence of single molecule manipulation techniques that structure can now be controlled by the application of stretching and torsional stresses. In this article we review some recent experiments on the stretching and twisting of single biopolymers, testing the elastic properties of DNA and proteins and studying their stress-induced structural transitions. Numerical simulations have emerged as a precious tool to interpret the experimental data and predict the associated structural changes. We shall explain how a combination of these experimental and computational tools open a new vista on the structure of biomolecules.