We discuss recent results in the theory of Journé operators with matrix weights. Those are biparameter Calderon-Zygmund operators. The corresponding scalar weighted estimates are due to R. Fefferman in the 1980's. We use a biparameter dyadic representation leading to paraproducts and product-BMO estimates. If time permits, we will explain the probabilistic interpretation of the $H^1$-BMO duality in the dyadic setting.