Laser-plasma accelerators have the potential to be a compact and widely available alternative to conventional accelerators for the next generation of particle colliders and light sources, such as X-ray free electron lasers. However, these accelerators are complex systems: they rely on the excitation of self-organized structures in the plasma in order to create accelerating fields. Present theory does not allow a full understanding of the associated complex laser-plasma interaction physics and this hinders unleashing the full potential of such accelerators. In this project a framework will be developed that will significantly advance our understanding and ability to control laser-plasma accelerators. The project will be centered around the detection and study of nonlinear coherent structures that are responsible for particle acceleration. The ability of such structures to support optimal particle acceleration will be studied in (1) simplified models of laser-plasma dynamics, (2) fully self-consistent simulations and (3) experimental data. The insights gained through these studies will lead to new methods to control laser-plasma acceleration by introducing well designed perturbations and to the development of real-time control methodologies for experiments. Particle in cell (PIC) simulations allow the self consistent study of the system of electromagnetic fields and particles in laser-plasma interaction. This allows the direct confrontation with experimental data and even the complete computational modeling of experimental techniques, as illustrated by the PI for the case of ultrafast shadowgraphy [Siminos et al Plasma Phys. Contr. Fusion 58 065004 (2016), Sävert et al, Phys. Rev. Lett. 115, 055002 (2015)]. This technique allowed the direct observation of nonlinear coherent structures in a laser-plasma system for the first time, while its computational modeling by the PI facilitated the interpretation of the observations. In this project the simulation of coherent structures will be further developed with an emphasis on their stability, selective excitation and implications for accelerated particle spectra. Apart from wakefields that have been extensively studied, we will also consider structures such as shocks and solitons. We will put an emphasis on possible experimental signatures of such structures, in particular using our computational shadowgraphy diagnostics. Comprehensive parametric studies of different interaction conditions will be performed in order to facilitate the design of future experiments.