In this paper, we develop a three-dimensional kinetic theory of longitudinal plasma oscillations in a relativistic electron beam. Our analysis includes the effects of betatronmotion, finite emittance, and energy spread as well as edge effects due to the finite size of the beam. The consequences of these effects are shown to be of significant interest, as they give rise to several distinct new phenomena. These include an emittance induced anisotropy between backward and forward propagating plasma waves as well as a beatwave effect between plasma and betatronoscillations caused by the coupling of betatronmotion to the transverse structure of the charge perturbation. The experimental implications of these new results and their relevance to the beam and radiation physics of advanced light sources, such as free-electron lasers, are also discussed.