Current high-power lasers can supply coherent pulses with petawatt peak powers and intensities sufficient to drive antimatter jets, produce bright x-ray radiation, and accelerate electrons and ions to relativistic velocities. The goal of our research is to develop and apply plasma-based sources of intense ultrafast (sub-picosecond) radiation across the electromagnetic spectrum. Here we discuss the creation of intense attosecond pulses using relativistic high harmonic generation from overdense plasma surfaces and plasma-based laser amplification using stimulated Raman and Brillouin scattering. Relativistic high harmonic generation offers a path to attosecond pulses of unprecedented intensity, allowing the study of non-linear optics in the attosecond regime. Raman and Brillouin amplification of laser pulses in plasma avoid the damage-threshold limits of current solid-state systems, potentially producing orders-of-magnitude improvements in peak power. Recent advances in understanding and improving the efficiency of these processes will be covered, with a particular emphasis on the use of particle-in-cell simulations.