This thesis reports on experimental and numerical investigations of ion acceleration employing high energy, picosecond laser pulses. In two separate campaigns on the petawatt arm of the Vulcan laser system, novel laser and target parameters were implemented to explore schemes of ion acceleration beyond the well established target normal sheath acceleration (TNSA) regime, namely radiation pressure acceleration (RPA) in the limits of thick (hole boring) and thin (light sail) target regimes. In the first experiment, a target composed of a solid cryogenic hydrogen ribbon, 75- 100μm in thickness, was irradiated with pulses containing an energy of 300J, focused at intensities up to 5e20 W/cm2 . Proton beams, with no detectable contaminants, are reported on several ion diagnostics - Thomson parabola spectrometers (TPS), radiochromic film (RCF), and time-of-flight (ToF) detectors. Energies approaching 60MeV are recorded in RCF stacks, and over 50MeV in the TPS, with an average energy comparable to what is achieved with 9μm plastic foils, also irradiated in this campaign for comparison. Two distinct proton beamlets are observed in the RCF for solid hydrogen, along the target normal, and laser axis directions, while plastic targets show only a single beam directed along target normal. In addition, the appearance of quasi-monoenergetic peaks, with 7% energy spread and primarily directed along the laser axis is observed for solid hydrogen, at an average energy of (34 ± 10)MeV. 2D PIC simulations are also presented, which show significant channelling and self-focusing in the solid hydrogen, greatly enhancing energies of protons accelerated via the hole boring mechanism, and explaining the appearance of the diverging beamlets seen in the RCF profiles for solid hydrogen. Self-focusing down to a width of approximately one laser wavelength, leading to intensities on the order of 1021W/cm2 is shown to occur independently of the existence of an underdense preplasma before the front of the target. The simulations also indicate the formation of a hot electron current filament at the end of the laser channel which propagates through the target and out of the rear side, generating a strong azimuthal magnetic field centred along an angle related to the laser incidence angle, and it is proposed that this may be responsible for the observation of monoenergetic features observed along a single angular direction. The second experiment investigated the irradiation of ultrathin (10-400nm) deuterated plastic (CD) and gold foils via a double pulse arrangement. Acceleration of ions via the light sail mechanism in ultrathin foils can be halted by the early onset of relativistically induced transparency (RIT). Suppression of the onset of RIT by a reduction in electron heating was investigated by the splitting of the main pulse into two equal intensity pulses, each containing ∼40% the energy of the main pulse, and temporally separating their arrival on the foil. A defocusing telescope was employed, allowing us to focus the second pulse at a point further along the laser axis from the foils front surface. An optimal arrangement of ∆T=4ps and ∆z=10μm, is reported for 85nm CD foils, achieving deuteron and proton spectral peak energies of 27MeV/n and 35MeV, respectively. This surpassed what was achieved by the single, full beam pulse on 85nm foils, despite containing 25% less laser energy, in a degraded focal spot, and was of comparable energy to the full beam pulse incident on the optimal thickness of 143nm, which achieved deuteron and proton energies of 29MeV/n and 40MeV, respectively. Neutron spectrometers were also employed in this campaign to diagnose the efficiency of the light sail phase, as neutrons are produced in CD targets during compression in the dense light sail front via the d(d,n)3He reaction. From the neutron energy and flux, the optimal double pulse arrangement for the light sail phase is shown to be ∆T=4ps and ∆z=10μm, in agreement with what was observed in the ion energies. Similarly, the proton spectral peak energy was seen to be optimised with a temporal delay of 2ps in the irradiation of 10nm gold foils. Neutron generation is also reported from gold foils, which is attributed to the (γ,n) photonuclear reaction. 2D PIC simulations using CD foils are presented, which show a peak in proton and deuteron energy for an optimal delay of 1.5τp, with an associated appearance of a high energy bunch at 40MeV/n in the deuteron spectra, that was not observed in the full beam simulation. A suppression of the onset of RIT is demonstrated when using the optimal double pulse arrangement, and the secondary pulses radiation pressure effect on the expanded, lower areal density target is posited as the origin of the deuteron bunching.