This thesis focuses on the propagation of charged particle beams in plasmas, and is divided into two main parts. In the second chapter, a novel theoretical model for underdense electron beam propagation during the nonlinear stage of the resistive Weibel instability (WI) is presented and is used to calculate the stopping time of the beam. The model and supporting simulation results lead to the conclusion that the WI initially enhances beam deceleration but then reduces it when compared to a filamentation-suppressed beam (without WI), so that the overall stopping time of the beam is essentially unaffected by the instability. Using the theoretical model, a criterion is derived that determines when deceleration is no longer enhanced by the instability. We also demonstrate that exotic plasma return current distributions can be obtained within and outside of beam filaments that sharply contrast those observed in collisionless systems. For example, the plasma return current is reversed in selected areas. In the next chapter, a new method for initiating the modulation instability (MI) of a proton beam in a proton driver plasma wakefield accelerator using a short laser pulse preceding the beam is presented. A diffracting laser pulse is used to produce a plasma wave that provides a seeding modulation of the proton bunch with the period equal to that of the plasma wave. Using the envelope description of the proton beam, this method of seeding the MI is analytically compared with the earlier suggested seeding technique that involves an abrupt truncation of the proton bunch. The full kinetic simulation of a realistic proton bunch is used to validate the analytic results. It is further used to demonstrate that a plasma density ramp placed in the early stages of the laser-seeded MI leads to its stabilization, resulting in sustained accelerating electric fields (of order several hundred MV/m) over long propagation distances (100-1000 m). The final chapter describes a harmonic expansion formalism that attempts to explain the post-linear stage of the MI. The formalism is developed first, and then several crippling problems with it are identified. / text