Suspensions are dispersions of solid particles in liquids. A remarkable property of dense (concentrated) suspensions is that they can transform from liquid-like at rest to solid-like under sudden impact, and back to liquid-like when the applied stress is removed. Previous work showed that this impact-induced solidification involves rapidly moving jamming fronts. Furthermore, dense suspensions can solidify not only under impact, but also under sudden extension or shear. However, compared to the intensively studied steady-state rheology, these transient dynamics of dense suspensions are still poorly understood, and many details of the sudden solidification process have remained unresolved. ,In this thesis we use high-speed ultrasound imaging to probe non-invasively how the interior of a dense suspension responds to impact. Measuring the speed of sound we demonstrate that the solidification proceeds without any detectable increase in packing fraction, and imaging the evolving flow field we find that the shear intensity is maximized right at the jamming front. Taken together, this provides direct experimental evidence for jamming by shear, rather than densification, as driving the transformation. ,To develop a quantitative description of such transient flows, we then study the fronts that appear when dense suspensions are subjected to sudden shear in a quasi-one-dimensional system. We extract the front propagation speed, local shear rate, and stress distributions from the flow field, and map out their dependence on boundary conditions and packing fraction. We show that the experimental findings can be explained by generalizing a phenomenological model originally developed to describe steady-state rheology. This is achieved by introducing a sole additional parameter: the characteristic strain scale that controls the crossover from start-up response to steady-state behavior. Finally, taking advantage of the fact that the shear fronts operate at fixed stress, we are able to map out properties of suspensions in the shear jamming regime, which is difficult if not impossible with standard steady-state rheology.