Three pump-3ω-probe Doppler-shift spectroscopy experiments are presented along with both 1D radiation-hydrodynamics modelling (HYADES) and 1D three-stage modelling process involving: HYADES radiation-hydrodynamics pre-pulse calculations; EPOCH kinetic particle-in-cell main-pulse calculation initialised from HYADES result; followed by hydrodynamic calculations, initialised from EPOCH result, of the evolution after the main-pulse. These investigations are aimed at exploring the formation of shocks at the front surface of targets after interaction with an ultra-short (30 fs), ultra-intense (10^18 W/cm^2 ) laser pulse. To this end a 3ω-probe is delayed then reflected from a 3ω critical surface on the front surface to obtain a temporal profile of the velocity of this surface. Two investigations use identical polished crown glass targets, but are performed with lasers systems with different contrast ratios (10^5 and 10^7 ). HYADES simulations match experimental results for the high contrast experiments except at early times. HYADES simulations of low contrast experiments do not agree. The three-step modelling process shows good agreement with experimental results in both cases, though with some adjustment to the pre-plasma scale-length for the low contrast case. The third Doppler-spectroscopy experiment uses a low density (over-dense) foam target with identical setup to high-contrast case described. Experimental results show a similar magnitude Doppler-shift evolution as in low-contrast case. HYADES simulations show similarities to experimental results but not overall trend. The three-step modelling process shows that the experimental response may be due to post-soliton formation as a result of SRS or photon acceleration plasma instabilities. This is supported by an additional 2D EPOCH simulation. A fourth theoretical investigation is presented into the transport of fast electrons produced 10^19−20 W/cm^2 laser pulses using the hybrid code ZEPHYROS. A low resistivity (< 5 µωm) at low temperatures (1 eV) is found to be of critical importance to suppressing filamentation of electron beams through low-Z targets.