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The Review Article by G. Tkachov and E. M. Hankiewicz (pp. 215–232) is focused on transport phenomena in topological insulators. This novel class of materials is distinct from conventional band insulators and conductors by the topologically nontrivial band structure that gives rise to unusual transport properties. In a topological insulator the character of electron transport varies from insulating in the interior of the material to metallic near its surface. Unlike, however, ordinary metals, the conducting surface states are topologically protected and characterized by spin helicity whereby the direction of the electron spin is locked to the momentum direction. Owing to these properties, topological insulators have been considered as platforms for many intriguing applications, ranging from spintronics to topological quantum information processing. The authors review topics of the most active theoretical and experimental research on transport and related phenomena in two- and three-dimensional topological insulators. In particular, the review provides a focused introductory discussion of the quantum spin Hall effect, weak antilocalization, the half-integer quantum Hall effect, mixed s- and p-wave induced superconductivity, superconducting Klein tunneling, topological Andreev bound states and related Majorana midgap states in topological insulators.