Curved pipes are essential components of nearly all the industrial process equipments, ranging from power production, chemical and food industries, heat exchangers, nuclear reactors, or exhaust gas ducts of engines. During the last two decades, an interest on turbulent flows in such conduits has revived, probably due to their connection to technical applications such as cooling systems of nuclear reactors (e.g., safety issues due to flow-induced fatigue) and reciprocating engines (e.g., efficiency optimization through exhaust gas treatment in pulsatile turbulent flows). The present review paper, therefore, is an account on the state-of-the-art research concerning turbulent flow in curved pipes, naturally covering mostly experimental work, while also analytical and numerical works are reviewed. This paper starts with a historical review on pipe flows in general and specifically on flows through curved conduits. In particular, research dealing with the effect of curvature on transition to turbulence, work dealing with pressure losses in curved pipes, as well as turbulence statistics are summarized. The swirl-switching phenomenon, a specific structural phenomenon occurring in turbulent curved pipe flows, which has interesting fundamental as well as practical implications, is reviewed. Additional complications, with respect to flow through bends, namely, entering swirling flow and pulsating flow, are reviewed as well. This review closes with a summary on the main literature body as well as an outlook on future work that should be performed in order to tackle open questions remaining in the field.