The interaction of high intensity laser pulses with matter is of current research interest not only for potential applications but also due to the interesting non-linear process that can occur with current experimental facilities. Understanding many of the non-linear processes requires significant modeling and simulation effort. We explore several aspects of laser pulse evolution and plasma response in simulations ranging from modeling laser wakefield accelerators to modeling basic ionization processes. First, we present a model that describes the onset and growth of axial modulation found experimentally during the formation of plasma channels formed using an axicon lens. We provide a systematic development that describes this new type of parametric instability and explains the pressure dependence and the mechanism for formation of these axial modulations in the channel. Next, we describe details of a new three-dimensional laser pulse evolution code that we have developed to model propagation in tenuous gas and plasma and we provide relevant information about the validation and testing of the code. We then use this new code to examine the three-dimensional structure of the laser pulse evolving in the presence of ionizing gas. In particular we present results from the first three-dimensional study of the ionization scattering instability. Finally, we examine injecting electrons into laser wakefield accelerators. We examine in detail the injection and trapping characteristics for an electron beam with an initially broad energy distribution and look at the effect of beam loading on the trapping efficiency. We present estimates for the maximum charge that can be trapped from a low energy beam with a Boltzmann type energy distribution.