abstract: Our aim is to uncover specific structures that in some sense are dominating the behavior of complex and possibly high-dimensional dynamical systems — doing this from a finite set of full or partial observations of the system’s trajectories. We shall start with manifold-learning aided transition matrix analysis of Rayleigh-Bénard convection experiment, then discuss how coherent sets and associated „mixing coordinates“ can be revealed in non-autonomous flows, and finally propose a concept of measuring farness of trajectories with respect to dynamical mixing.