  This paper provides a review of some recent issues on the Mixmaster dynamics
concerning the features of its stochasticity. After a description of the
geometrical structure characterizing the homogeneous cosmological models in the
Bianchi classification and the Belinsky-Khalatnikov-Lifshitz piecewise
representation of the types VIII and IX oscillatory regime, we face the
question regarding the time covariance of the resulting chaos as viewed in
terms of continuous Misner-Chitr\'e like variables. Finally we show how in the
statistical mechanics framework the Mixmaster chaos raises as semiclassical
limit of the quantum dynamics in the Planckian era.
