Force-induced stretching of polymers is important in a variety of contexts. We have used theory and simulations to describe the response of homopolymers, with N monomers, to an external force (f) in good and poor solvents. In good solvents and for sufficiently large N we show, in accord with scaling predictions, that the mean extension along the f axis < Z > similar to f for small f and < Z > similar to f(2/3) (the Pincus regime) for intermediate values of f. The theoretical predictions for < Z > as a function off are in excellent agreement with simulations for N = 100 and 1600. However, even with N = 1600, the expected Pincus regime is not observed due to the breakdown of the assumptions in the blob picture for finite N. We predict the Pincus scaling in a good solvent will be observed for N greater than or similar to 10(5). The force-dependent structure factors for a polymer in a poor solvent show that there is a hierarchy of structures, depending on the nature of the solvent. For a weakly hydrophobic polymer, various structures (ideal conformations, self-avoiding chains, globules, and rods) emerge on distinct length scales as f is varied. A strongly hydrophobic polymer remains globular as long as f is less than a critical value f(c). Above f(c), an abrupt first-order transition to a rodlike structure occurs. Our predictions can be tested using single molecule experiments.