This work presents a method for the computation of electron energy loss spectra for large systems using the onetep code. The foundations of density functional theory will be discussed, with a focus on the linear scaling methods employed by onetep. A method for the prediction of spectra will be shown, with emphasis on the construction of the matrix elements needed. This method is tested against both other DFT codes and experiment. Once the ability of onetep to predict EEL spectra has been established the code is used to predict the spectra associated with oxygen vacancy defects in the anatase (101) surface. These spectra are found to agree with the limited experimental data available. EEL spectra for nitrogen dopants in anatase are also predicted, based on literature geometries for these. The energetics of the oxygen vacancy is also explored, using the ability of onetep to perform calculations on large cells to address elastic finite size effects and employing a correction scheme to remove electrostatic finite size effects. Finally, the properties of an extended grain boundaries defect in GaAs were investigated, focussing on properties relevant for optoelectronics.