Particle settling velocity is a fundamental parameter in sedimentology and engineering, and has accordingly received much attention in the literature. Grain properties, such as shape and drag coefficient, which affect terminal settling velocity, also control the threshold of initiation of motion and sediment entrainment into suspension. Terminal settling velocity therefore provides insights into sediment dynamics in modern and past depositional environments and is important for marine engineering works. Despite the global importance of resedimented carbonates the study of particle hydrodynamics is strongly biased towards terrigenous sediments. This paper presents a review of the settling hydrodynamics of carbonate grains and associated particle properties, such as shape, grain size and density. For carbonate grains these parameters are more complex than for siliciclastic counterparts due to their common biogenic origin, introducing a wide range of morphologies, densities and abrasion products as a result of the skeletal nature of such grains. This review includes an extensive database of published composition-specific settling velocities, as well as densities of common carbonate constituents. The database includes corals, coralline red algae, bivalves, brachiopods, gastropods, Halimeda green algae, bryozoans, crinoids, echinoderms, Alcyonarian spicules, numerous benthic and planktic foraminifers, and fecal pellets. Grain density as a function of skeletal structure and mineralogy exerts another control on settling velocity, with unclarity in density definitions hampering effective communication in the literature. The variation in single-grain hydrodynamic behaviour implies careful application of previously proposed equations for the prediction of settling velocity of bulk sand. Despite a firm basis there is a need for additional systematic composition-specific investigations to enable the adequate prediction of carbonate particle hydrodynamics due to the broad spectrum of forms and densities. Emerging technologies such as automated particle velocimetry, computational fluid dynamics, machine learning and microtomography provide exciting avenues for future understanding of the hydrodynamic behaviour of particles with the complexity of natural carbonate grains.