In many modern devices it is necessary to combine semiconducting properties with a wide energy band gap, whether for transparent conducting materials in touch screens, light emitting diodes operating in the blue or UV range, or energy applications such as collector layers in solar cells or photocatalytically active systems for water splitting. With such a combination there is a delicate balance between electronic disorder, as seen in conventional semiconductors, and ionic disorder, more prevalent in insulators. This balance is governed by the defect chemistry of the system, which is challenging to analyse at the atomic scale experimentally, allowing computational approaches to provide key insights. In this presentation I will discuss the hybrid quantum mechanical/molecular mechanical (QM/MM) embedded cluster approach to modelling defects in wide-gap semiconductors. I will discuss the advantages of this approach, such as the lack of periodic image charge interactions and an unambiguous reference energy to facilitate ionisation energy calculations, as well as the disadvantages. I will demonstrate the effectiveness of hybrid QM/MM by discussing band alignment in different polymorphs of TiO$_2$ (a photocatalytic water splitter), p-type doping in GaN (a key component of blue LEDs) and the role of oxygen vacancies in the three most common transparent conducting oxides (In$_2$O$_3$, ZnO and SnO$_2$).