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This paper reviews recent advances in continuous-time quantum walks (CTQW)and their application to transport in various systems. The introduction gives abrief survey of the historical background of CTQW. After a short outline of thetheoretical ideas behind CTQW and of its relation to classical continuous-timerandom walks (CTRW) in Sec.~2, implications for the efficiency of the transportare presented in Sec.~3. The fourth section gives an overview of differenttypes of networks on which CTQW have been studied so far. Extensions of CTQW tosystems with long-range interactions and with static disorder are discussed insection V. Systems with traps, i.e., systems in which the walker's probabilityto remain inside the system is not conserved, are presented in section IV.Relations to similar approaches to the transport are studied in section VII.The paper closes with an outlook on possible future directions.

Continuous-Time Quantum Walks: Models for Coherent Transport on Complex Networks