Frequently, DNA in vivo is organized into loops that are partially underwound and consequently form interwound helical supercoils. Methods from polymer statistical mechanics are used to show how the competition between entropy (thermal fluctuations) and elastic energy determines supercoil radius and pitch, in good agreement with recent experiments and simulations. Supercoil reorganization by means of slithering (reptation) of the DNA along the supercoil is argued to be a slow process. Extension of supercoiled DNA by an applied force shows a number of unexpected features, including coexistence of interwound and helical states.