Dyke injection transports large volumes of magma over great distances, controlling the supply of magma to volcanoes and effectively releasing tensional stress at divergent plate margins. This thesis aims to improve understanding of dyke injection processes on different scales. Dyke shapes measured on the Isle of Rum have been analysed and show a mismatch between the currently accepted theory used to describe their shape, and the measured data. The measured dykes show wider edges than expected, consistent with wedging and cooling of magma in the dyke tips; wedged dykes can act as conduits for longer. Finite difference one- and two-dimensional models for the thermal evolution of the crust due to heat transfer from multiple dyke injection have been developed and applied to the geological setting of the actively spreading Main Ethiopian and Red Sea rifts, where the spreading rates are 5 and 16 mm yr-1 respectively. The model has shown that the spreading rate is the first order control on the temperature build up. Differences in crustal thickness exist between these two regions; the crust has thinned under the Red Sea Rift whilst under the Main Ethiopian Rift there has been no appreciable thinning. This difference has led to the conclusion that the spreading rate, and thus the temperature profile, is the principal cause for the differences in crustal thicknesses. Above the brittle-ductile transition temperature, the crust is likely to undergo pre- dominantly ductile deformation; for slow spreading rates (e.g. 5 mm yr-1), it takes up to 142 ka for the dyke injection site to reach this temperature. The position of the locus of strain at an actively rifting margin migrates with time. For slow spreading rates, the strain locus must remain fixed for at least 142 ka before appreciable crustal heating allows the onset of ductile stretching. Where the spreading rate is faster, the locus of strain must remain fixed for shorter lengths of time. Thus Ethiopia's evolving locus of strain and low spreading rate have likely caused much of the extension to be accommodated by magmatic intrusion rather than by stretching. Comparisons between the thermal model results and geophysical observations from a segment of the Red Sea rift have been made. The mag- netotelluric survey across the rift axis of the actively spreading Red Sea Rift segment has shown two bodies of hot material; one explanation is that the rift axis has jumped. Scaled experimental models have been used to study multiple dyke injection in an extensional tectonic setting. For a fixed overpressure, larger spacings between injections give smaller rotation angles between injections. This is consistent with the rotation angles and injection spacings observed between the recent dyke injections on the Red Sea Rift.