GaN power devices are promising candidates for the next generation of high efficiency power semiconductor devices. Their material and device properties enable power conversion systems that are potentially smaller, lighter, less complex, cheaper and more efficient than silicon based solutions. While GaN-based HEMTs are now available on the market, the physics of the device are not yet fully understood and there is still ample margin to improve the electrical characteristics and develop new operating capabilities. The work reported in this thesis is concerned with the characterization, modelling and design of GaN based HEMTs. The research performed is the result of a collaboration with International Rectifier (now Infineon Technologies). While the typical devices under consideration in this thesis have been analysed from diverse perspectives, the main research topics addressed are (i) substrate leakage, (ii) buffer and trap modelling and (iii) hole injection effects. Characterization has been performed on small and large area test structures and transistors by means of static and dynamic measurements. Based on temperature dependent leakage measurements, the essential characteristics of vertical leakage were modelled, leading to the conclusion that the substrate and its interface with the nucleation layer can potentially control its magnitude. Backgating measurement techniques have been employed to characterize buffer traps and an ad hoc TCAD model has been developed to evaluate different modelling approaches. Inconsistencies between existing models were highlighted and a qualitative correlation was found between vertical leakage and trapping. Similar experimental techniques have been used to analyse the effect of hole injection in a GaN HEMT featuring a p GaN-type gate. It was found that the decrease in drain current associated with the substrate coupling effect is virtually suppressed, if sufficient holes are injected from the gate. The voltage and time dependencies of the drain current recovery were also investigated, and it was concluded that, while high voltages should not be a concern, careful optimization of the device toward substrate coupling immunity may be needed to operate simultaneously at high voltages and high frequencies. Finally, novel device structures and technical solutions have been proposed to improve the characteristics of GaN based HEMTs.