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We review theoretical and experimental highlights in transport intwo-dimensional materials focussing on key developments over the last fiveyears. Topological insulators are finding applications in magnetic devices,while Hall transport in doped samples and the general issue of topologicalprotection remain controversial. In transition metal dichalcogenidesvalley-dependent electrical and optical phenomena continue to stimulatestate-of-the-art experiments. In Weyl semimetals the properties of Fermi arcsare being actively investigated. A new field, expected to grow in the nearfuture, focuses on the non-linear electrical and optical responses oftopological materials, where fundamental questions are once more being askedabout the intertwining roles of the Berry curvature and disorder scattering. Intopological superconductors the quest for chiral superconductivity, Majoranafermions and topological quantum computing is continuing apace.

Transport in two-dimensional topological materials: recent developments in experiment and theory