In my talk I discuss several aspects of transport phenomena in the near-integrable multiscale dynamical systems. I will start with an introduction into what makes a system chaotic and how these properties can be quantified. In the next part of the talk I consider mixing via resonances-induced chaotic advection in volume-preserving flows. I show that proper characterization of the mixing quality requires introduction of two different metrics. The first metric determines the relative volumes of the domain of chaotic streamlines and the domain of regular streamlines. The second metric describes the time for homogenization inside the chaotic domain. In the last part of the talk I illustrate how the capture into resonance, that by itself is random in nature and, consequently, is rather inefficient as a mechanism of regular transport, can be structured with little additional cost. As a model problem I consider the Hamiltonian dynamics of a charged particle in an electromagnetic field.