  We review recent developments of slow/fast stochastic differential equations,
and also present a new result on
  Diffusion Homogenisation Theory with fractional and non-strong-mixing noise
and providing new examples.
  The emphasise of the review will be on the recently developed effective
dynamic theory for two scale random systems with fractional noise: Stochastic
Averaging and `Rough Diffusion Homogenisation Theory'. We also study the
geometric models with perturbations to symmetries.
