The literature on the structure and behaviour of gravity currents is reviewed, with emphasis on some recent studies, and with particular attention to turbidity currents, though reference is also made to comparable behaviour in pyroclastic flows. Questions of definition are discussed, in particular the distinction between dense currents, which may deposit en masse, and more dilute currents. High-density dispersions may exist as a discrete, independently moving layer beneath a more dilute flow, as the basal part of a continuous density distribution or possibly as a transient depositional layer. Existing theory appears inadequate to explain the behaviour of some high-density dispersions. Surge-type currents are contrasted with quasi-steady currents, which may be generated by a variety of mechanisms including direct feed by rivers in flood. Such fluvially generated currents provide one means of generating currents with reversing buoyancy. Geologically significant turbidity currents are impractical for direct study owing to their large scale and (often) destructive nature. Small-scale laboratory currents offer a wealth of insights into turbidity current behaviour. This paper summarizes recent experimental studies that focus on the physical structure of gravity currents, with emphasis on the velocity and turbulence structure, the vertical density distribution and the stability of stratification. Preliminary quantification of the turbulence structure (including controls on turbulent entrainment, turbulent kinetic energy, Reynolds stresses and turbulence production) has been facilitated by recent technological developments that have allowed the measurement of instantaneous fluctuations in both velocity and concentration. Laboratory models, however, generally involve substantial simplification, and require compromises in some parameters to achieve adequate scaling of the parameters of most interest. Mathematical modelling also provides important insights into turbidity current behaviour. We discuss various approaches to modelling, ranging from simple hydraulic equations to systems of partial differential equations that explicitly treat conservation of momentum, fluid and sediment mass, and turbulent kinetic energy. The application for which the model is designed (i.e. to calculate mean head velocity or to create an instantaneous two-dimensional contour plot of downstream velocity in a current) determines the complexity of the mathematical model required. The behaviour of suspension currents around topography is complex and depends upon the relative height of the topography, and upon the density and velocity structure of the current. Many interactions with topography are well described by the internal Froude number, Fri. Both reflection and deflection of currents may occur on the upstream side of topography, depending upon Fri. On the downstream side of topography, flow separation, lee waves or hydraulic jumps may occur.