Turbulence in fluids and plasmas is one of the least understood topics in classical continuum physics. The problem addresses randomly varying flows, where individual realizations are too complicated to be comprehensible, but which can be described and analysed by statistical methods. In spite of significant progress in the studies of neutral flows (in water etc.), there are still several basic problems, which are not fully understood. As far as plasmas are concerned (i.e. gases composed of charged particles) the situation is even more unfavourable. In this case the sensitivity of the gas to electric and magnetic fields adds to the complexity, and progress has only been made by significant simplifications, which are not always justifiable. It is however quite important that we improve our understanding of turbulent plasmas, since most of the matter on astrophysical and heliospheric scales is in the plasma state, and is often found to be strongly turbulent. One of the most important properties of turbulent fluctuations in gases and fluids is their ability to disperse particles at an anomalously large rate. This implies that boundaries in space are maintained only to the extent allowed by turbulent transport. Similarly, it is found that the electrical conductivity of a plasma is often controlled by turbulence. This latter problem is studied even less than turbulent transport, but it is expected to be central for the understanding of the large scale current systems associated with the Earth's magnetosphere. The research group will address selected central questions concerning turbulent transport, with emphasis on applications in nature.