© 2016 Institute of Materials, Minerals and Mining. The formation of topologically close-packed (TCP) phases in nickel-base superalloys is an issue of increasing importance as alloys are designed with higher refractory element contents to meet the requirements of next generation turbine engines. This review considers the factors that affect an alloy’s susceptibility to TCP formation. In particular, the debate surrounding the effect of certain individual elements, such as Co and Re, in promoting or suppressing TCP formation is examined alongside the various mechanisms that have been proposed to account for this behaviour. In addition, the detrimental effects of these phases on the alloy’s mechanical properties are discussed, including crack initiation at precipitates, depletion of solid solution strengthening refractory elements and the effect on γ/γ′ rafting behaviour. This review was chosen as a runner up of the 2016 Materials Literature Review Prize of the Institute of Materials, Minerals and Mining, run by the Editorial Board of MST. Sponsorship of the prize by TWI Ltd is gratefully acknowledged.