Stochastic delay differential equations often arise in biosciences as models involving, e.g., negative feedback terms and intrinsic or extrinsic noise. Examples of applications range from stochastic models of human immune response systems, neural networks or neural fields to genetic regulatory systems. Stability theory for stochastic delay differential equations is quite well established and we will provide a brief review of available methods and results. Stochastic dynamical systems theory for stochastic delay differential equations beyond the stability analysis of equilibria is much less developed and we will report on some open problems in this area.