The appearance of the first luminous sources in the Universe marks the beginning of the epoch of reionisation. The cosmic reionisation of hydrogen has been the last major phase transition in the... Show moreThe appearance of the first luminous sources in the Universe marks the beginning of the epoch of reionisation. The cosmic reionisation of hydrogen has been the last major phase transition in the evolution of the Universe, turning cool neutral gas into the hot, ionised plasma we observe today. Up to now, direct observations of reionisation have been impossible, most of our current knowledge therefore stems from numerical studies. However, even with current computing facilities the modelling of the reionisation epoch presents some serious challenges. Radiative transfer is perhaps the biggest challenge, due to the high dimensionality and non-locality of the problem. In this thesis the latest improvements of the SimpleX method, that was designed to overcome some of the problems related to radiative transfer, are presented. We have used this method to study the escape fraction of ionising photons from galaxies. Our results show that high-redshift dwarf galaxies can be important contributors to cosmic reionisation. In addition, we have studied the effect of the inclusion of diffuse recombination radiation in reionisation simulations on large scales, which has been neglected by recent studies. We show that diffuse recombination radiation does not have a significant influence on the reionisation process. Show less