In this report, we review the results of our joint experimental and theoretical studies of electron-interference, and interaction, phenomena in open electron cavities known as quantum dots. The transport through these structures is shown to be heavily influenced by the remnants of their discrete density of states, elements of which remain resolved in spite of the strong coupling that exists between the cavity and its reservoirs. The experimental signatures of this density of states are discussed at length in this report, and are shown to be related to characteristic wavefunction scarring, involving a small number of classical orbits. A semiclassical analysis of this behaviour shows it to be related to the effect of dynamical tunnelling, in which electrons are injected into the dot tunnel through classically forbidden regions of phase space, to access isolated regular orbits. The dynamical tunnelling gives rise to the formation of long-lived quasi-bound states in the open dots, and the many-body implications associated with electron charging at these resonances are also explored in this report.