Stochastic simulation techniques play an important role in investigating polymer dynamics. Such simulations can be made more efficient by applying variance reduction methods. We present and compare various variance reduction schemes, based either on importance sampling strategies or on the use of control variates. In order to demonstrate that variance reduced simulations are a powerful tool in polymer kinetic theory, we show that for Hookean dumbbells with hydrodynamic interaction up to two orders in computer time can be saved uniformly in time.