Many flows in nature are subject to a complex interplay between viscous, elastic and capillary forces, all of which may couple to varying degrees resulting in elaborate dynamical phenomena. In this journal format thesis, we present detailed experimental studies of two different systems, each showcasing fundamental aspects of elastohydrodynamic and capillary flows. We begin with an investigation of displacement flows within an elasto-rigid channel, comprising a rigid shallow channel topped with an elastic membrane. Initially filled with viscous oil and partially drained to collapse the upper membrane, we reopen the channel via the injection of air at constant volumetric flow rate. Air propagates along the length of the channel as a single continuous `finger', working against viscous, capillary and elastic forces. When the channel is initially strongly collapsed, such that the membrane almost contacts the rigid base, we observe two different behaviours at low and high flow speeds, which correspond to viscous- and elastic-dominated reopening dynamics. Over an intermediate range of flow speeds, we observe transient evolution in terms of finger speed and bubble pressure towards high or low speed reopening behaviours. Through direct observation of the evolving finger morphology along with speed and pressure measurements, we infer the existence of unstable propagation modes which orchestrate the system's unsteady dynamics. We then investigate the importance of elasto-capillary effects in compliant vessels over a range of initial collapse and flow speed. Direct comparison with the simulations of a depth-averaged model provides greater insight into some of the underlying dynamics of reopening, as well as serving to validate aspects of the model. The second problem studied is an idealised system for droplet-substrate interactions: an aqueous droplet deposited on the surface of a deep layer of immiscible viscous liquid. We consider substrate liquids which wet the droplet perfectly, spreading to cover the droplet surface and engulfing the droplet as a consequence. We study the dynamical process of droplet engulfment, focussing on the effects of varying droplet volume and substrate viscosity. We reveal the central role played by gravity for even microscopic droplets, and find that droplets of intermediate size within the range studied take the longest time to be engulfed.