Dynamical systems with delayed feedback often exhibit complex oscillations not observed in analogous systems without delay. Stochastic effects can change the picture dramatically, particularly if multiple time scales are present. Then transients ignored in the deterministic system can dominate the long range behavior. This talk will contrast the effects of different noise sources in certain systems with delayed feedback. We show how ideas from canonical physical and mechanical systems can be applied in biological models for disease and balance. The approaches we consider capture the effects of noise and delay in the contexts of piecewise smooth systems, nonlinearities, and discontinuities.