Geophysical gravity-driven flows -- including avalanches, debris flows, pyroclastic flows and submarine turbidity currents -- are multiphase natural hazards that flow under the influence of gravity. Despite their differences, they share much of the same physics, having the potential to pick up material from beneath, a process called basal entrainment during which the flow may increase in volume and velocity manyfold. Due to their complexity and unpredictability there are still many unanswered questions about their mechanics, so that many of the theoretical models in use are based on insufficient data sets and may not apply to a general case. Here, basal entrainment by geophysical gravity-driven flows is studied by isolating the process in idealised laboratory experiments. The avalanche is simplified and controlled in such a way that any changes can be confidently attributed to the entrainment process alone. Further, the methods available in the laboratory allow the continuous, passive study of entrainment, so that for the first time full data sets of internal measurements are obtained, from experiments ranging from simple to complex. The data obtained is easily exploited for confirmation of the mathematical models developed in this thesis. Experiments which simulated entraining avalanches as Newtonian dam-breaks along a horizontal flume and as viscoplastic dam-breaks along an inclined flume both showed an increase in front position, dependent on the amount of material available, amongst other changes. The experimental results allow the development of a theoretical thin-film model in both cases which is solved numerically and compares favourably with the data obtained. The Newtonian model reproduced the flow characteristics excellently and the viscoplastic model successfully simulated the effects of entrainable material. The possibility of performing similar experiments using a granular suspension is also investigated, with promising results. This work shows that the effect of entrainment on gravity-driven flows can be quantified and modelled mathematically as a non-local transport process. This has implications for hazard modelling: if the quantity of available loose material is known, and its characteristics are similar to those of the flowing avalanche, the avalanche and the entrainable bed can be modelled as a continuous flow over a rigid base. Thus it is suggested that the models developed be tested in more realistic cases, e.g. in the case of an avalanche entraining material with different characteristics, or in a more complex geometry, in order to better mimic what happens in nature.