Proteins must self-assemble into specific structures in order to function correctly. Such 'folding' usually leads reliably to the correct structure, but can sometimes go awry. Misfolded proteins are thought to trigger a wide range of diseases, from Alzheimer's and Parkinson's to ALS, prion disorders, and diabetes, but the mechanisms by which native folding goes wrong to produce misfolded structures is poorly understood. I will discuss work on two misfolding-prone proteins, SOD1 and PrP, using laser tweezers to unfold and refold single molecules held under tension, showing how these measurements can be used to deduce folding and misfolding pathways. Studying SOD1, whose misfolding can cause ALS, we find that an isolated monomer folds via numerous intermediate states, corresponding to formation of each of the beta-strands in the native structure in sequence. Direct observation of misfolding events reveals that misfolding branches off from the native pathway at specific points, pinpointing the critical parts of the structure. We also find that a disease-causing point mutation increases the incidence of misfolding enormously, from 5% to 95%. Turning to PrP, which causes prion diseases, we compare the folding of PrP from species with different disease susceptibility, to seek clues for the origin of the differences. Very surprisingly, we find that--despite the almost identical sequences and structures of PrP from hamsters, rabbits, bank voles, and dogs--the folding of these proteins differs significantly in terms of the number of intermediate states traversed, the nature of the energy barriers between states, and the pathways followed. Comparison of the folding of PrP from different species suggests that higher energy barriers lead to greater disease susceptibility. This work shows how single-molecule approaches can be used to address long-standing problems in biology and medicine.