This thesis covers experimental and numerical studies on novel schemes of ion accelera- tion with high intensity lasers. In particular, it discusses previously unexplored regimes incorporating the radiation pressure of intense lasers. These schemes are of interest to potential applications due to the emergence of improved ion beam properties that are detailed in this thesis. The thesis discusses results from ion acceleration experiments using intense optical lasers on ultra-thin targets at the Rutherford Appleton Laboratory, where the Vulcan Petawatt system was used to irradiate nanometre thickness foils. In particular, the accelerated proton beam profiles from these interactions showed a variety of features, such as Rayleigh-Taylor-like instability driven spatial beam modulation, annular rings and a high-energy tail. A particularly interesting novel observation is the emergence of a spectrally peaked on-axis component to the proton beam, which is indicative of buffering of the proton layer ahead of a heating heavier ion species. These different features will be analysed and discussed, and modelled using PIC simulation. The thesis also includes the results from recent experiments studying the interaction of an intense CO2 laser with an overdense plasma generated by a gas jet. A remarkably monoenergetic proton beam was measured, in contrast to the majority of experiments performed previously on ion acceleration, and was found by optical probing and numer- ical simulation to be a result of hole-boring generated by the radiation pressure of the intense laser pulse acting on the plasma. The thesis will include analysis of interferometry and shadowgraphy images of the plasma, and discussion of the plasma dynamics and ion generation mechanisms involved, including the generation of radiation pressure driven collisionless shock waves. The effects of the laser prepulse, electron transport effects and non-linear post-soliton production will all be discussed. It will also present detailed numerical particle-in-cell (PIC) simulation of the interaction.