The first part of this paper provides an overview of the state of the art of the hydrodynamics of liquid suspensions of solid particles. It is shown that knowledge of the suspension Archimedes number is sufficient to estimate the voidage–velocity parameters for suspensions of solids possessing homogenous characteristics, thereby completely defining the system from a fluid dynamic point of view. A general relation is presented which will indicate if a solid–fluid system will be in the fixed or in the suspended state depending on the relative velocity between the two phases. Modifications of the previous approach when the solid particles are not spherical have been also indicated. The basic features of the pseudo-fluid approach are then presented. This approach is useful when the solids making up the suspension have different sizes: by the introduction of the pseudo-fluid apparent characteristics (density and viscosity) it is possible to make basic estimations of the suspension behaviour. The second part of the paper outlines possible application of suspension theory to geological phenomena, such as the vertical transport of water–sand suspensions. Aspects of interest are the minimum pressure required for the transport of the suspension, the estimation of suspension flow rate through an overall pressure balance, the vertical transport of large ‘breccia’ blocks and the behaviour of the solid particles present in the rising conduit once the overpressure falls below the minimum value needed to sustain the flow. Finally, a warning is given on the limitations of the presented relationships (e.g. the assumption of homogeneous solid dispersion in the suspension) and on situations such as inclined conduits which require a different approach.