In this paper we consider transport in a toroidal system with broken flux surfaces. Flux surfaces with rational field line winding number can degenerate and form magnetic islands. Where neighbouring chains of islands overlap, a region of chaotic field forms. Thus, the generic topology of the magnetic field in a toroidal device consists of an alternation of shells with 'good' surfaces and shells with islands or chaotic field.

In a chaotic field, a field line fills up a region of space and thus makes significant radial excursions. Particles following a chaotic field line may experience rapid radial transport. Recent experimental evidence for the existence of alternating layers with high and low thermal transport is presented. The implication for the determination of transport coefficients is discussed. It is shown that a transport analysis that does not resolve the fine structure of the transport coefficient yields results that are almost meaningless.