  We discuss uniform sampling algorithms that are based on stochastic growth
methods, using sampling of extreme configurations of polymers in simple lattice
models as a motivation. We shall show how a series of clever enhancements to a
fifty-odd year old algorithm, the Rosenbluth method, led to a cutting-edge
algorithm capable of uniform sampling of equilibrium statistical mechanical
systems of polymers in situations where competing algorithms failed to perform
well. Examples range from collapsed homo-polymers near sticky surfaces to
models of protein folding.
