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This thesis is dedicated to the investigation of laser-plasma particle acceleration concepts. Some of the work was focused on improving electron and proton acceleration for future applications, in terms of maximizing the particle energy and minimizing the divergence of the X-ray beams. In laser wakefield acceleration, a very intense laser pulse (> 1018 W/cm2) is focused in a gas. The leading edge of the pulse is intense enough to ionize the gas, and the main part of the pulse interacts with a plasma. Under the action of the ponderomotive force, the intense laser pulse can expel plasma electrons and form a wake in the plasma that trails the laser pulse. This charge separation leads to the formation of an ion cavity that results in electromagnetic fields several orders of magnitude stronger than those in conventional accelerators, up to TV/m. Some electrons can be accelerated to several hundred MeV over distances of less than a cm by injecting them into the plasma wake. There are also focusing forces inside the plasma wake, and the injected electrons will oscillate transversely about the optical axis, producing multi-keV betatron X-ray radiation. This radiation is directed along the optical axis with a low divergence of a few tens of mrad. One application investigated in this work was the possibility of using laser-wakefield-accelerated electrons for very high-energy electron (VHEE) radiotherapy. High-energy electrons can reach deep tumours with limited scattering, and have a more suitable dose-depth profile than photon beams. In this work, a VHEE beam was focused inside a phantom using electromagnetic quadrupoles to mimic stereotactic radiotherapy. The X-ray beam generated by LWFA was used to measure the equivalent path length and 3D liquid mass distribution in commercial fuel injectors by tomographic reconstruction. It was shown that the sensitivity (in terms of the detectable liquid mass) was comparable to that possible with large synchrotron facilities. Furthermor