Seafloor sediment flows, called turbidity currents, form the largest sediment accumulations, deepest canyons and longest channels on Earth. It was once thought that turbidity currents were impractical to measure in action, especially given their ability to damage sensors in their path, but direct monitoring since the mid-2010s has measured them in detail. In this Review, we summarize knowledge of turbidity currents gleaned from this direct monitoring. Monitoring identifies triggering mechanisms from dilute river plumes, and shows how rapid sediment accumulation can precondition slope failure, but the final triggers can be delayed and subtle. Turbidity currents are consistently more frequent than predicted by past sequence-stratigraphic models, including at sites >300 km from any coast. Faster flows (more than ~1.5 m s–1) are driven by a dense near-bed layer at their front, whereas slower flows are entirely dilute. This frontal layer sometimes erodes large (>2.5 km3) volumes of sediment, yet maintains a near-uniform speed, leading to a travelling-wave model. Monitoring shows that flows sculpt canyons and channels through fast-moving knickpoints, and shows how deposits originate. Emerging technologies with reduced cost and risk can lead to widespread monitoring of turbidity currents, so their sediment and carbon fluxes can be compared with other major global transport processes.