Given a density f on Euclidean k-space and a starting point x, choose a line L at random through x and move to a point on L chosen at random from f restricted to L. This procedure defines a Markov chain-- the "hit and run process." The given density f is stationary; for almost all starting points x, the distribution of the chain at time n converges to the stationary distribution as n gets large. This expository paper proves some of the convergence theorems, and gives examples.