Space charge has been recognized as an important factor contributing to the electrical failure of the cable insulation. Extensive efforts have been made to investigate space charge dynamics within polymeric insulations under electric stresses. Basic information about space charge has been recognized resorting to modern charge mapping techniques but the underlying mechanisms for charge transport, charge trapping characteristics are not yet well understood. Hence theoretical modelling and numerical simulation are employed to simulate the space charge and provide an insight into the charge distribution in dielectrics. This thesis comprises the quantitative analysis of space charge through numerical modelling and experimental investigations of charge trapping in polymeric insulation materials. A bipolar charge transport model which involves bipolar charge injection from the electrodes, charge transport with trapping and recombination in the bulk has been developed to simulate the dynamics of space charge in polyethylene. The build-up of space charge in polyethylene under dc electric fields has been modelled. The influence of parameters related to the properties of polyethylene on the formation of space charge has been recognized. Furthermore, this model is introduced to simulate the dynamics of corona charge decay in polyethylene. The formation of charge packets in polyethylene is also investigated using a numerical modelling approach. A fast pulsed electro-acoustic system along with a data processing program has been developed to investigate the behaviour of space charge in polyethylene under ac voltages. The understanding of space charge under ac stresses has also been simulated using the further developed bipolar charge transport model. Experiments and simulation have also been expanded into understanding electroluminescence, which is an indication of pre-aging of polymers under ac stress.