The insulated gate bipolar transistor (IGBT) is arguably the most important device currently used in power conversion at medium to high levels. This thesis presents a detailed analysis of IGBT and freewheel diode operation in the context of inductive switching, which accounts for the majority of power conversion processes. In particular, the consequences of the device behaviour on device and circuit interaction are examined. The behaviour of one device is shown to be tightly coupled to that of the other device and the circuit elements during switching. Performance, reliability, efficiency and cost are all affected by design considerations arising from the interaction of switching devices in power converters. Thus there is an incentive to ensure that the designs of devices and circuits are matched, allowing the requirements of the system as a whole to be satisfied. To achieve this, a formal numerical optimisation technique is used in conjunction with compact device models to offer a novel alternative to design iteration using finite-element simulators. Despite their perceived accuracy, these suffer from severe computational requirements and therefore offer limited ability to explore large areas of device design. The development of compact device models possessing a combination of high simulation speed and predictable accuracy was required, so that practical optimisation may take place. An example of device optimisation has shown that there is indeed insight to be gained in optimising the devices and circuit as a whole. The optimisation has the potential to investigate aspects of device operation, such as active gate drive circuits, in addition to device aspects such as device geometry. A useful example of device optimisation is given in the form of automated parameter extraction, where device parameters are optimised to match simulated results with experimental results. This allows designers to have greater confidence in device models used for converter circuit design. The future potential of optimisation is greater still, considering the advances made in handling multiple objectives and uncertainty in operating conditions. Conclusions are drawn concerning the development of IGBTs, diodes and circuits.