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The reliability issues of AlGaN/GaN HEMTs for power and RF applications have attracted much attention from the research community in order to improve their application range. In this thesis, multiple reliability issues of AlGaN/GaN HEMTs are covered with detailed characterizations, simulations and analysis, which include hard-switching, trapping effects, breakdown and gate leakages. By comparing a set of wafers with different SiNx passivation stoichiometries, HEMTs with Si-rich passivation layer stand out and show negligible dynamic ON-resistance after stress. In measurements of the hard- and soft-switching with tens of nano seconds switching time, it turned out that hard-switching would lead to significant self-heating and produce hot electrons. However, the temperature cools down after a few hundreds nano seconds after the switching while the surface charge trapping is the dominant reason for the dynamic ON-resistance increase. The study of multiple types of stress including ON-state, OFF-state and substrate bias were performed on the same devices. The dynamic ON-resistance shows a 60% increase after the ON-state stress compared to OFF-state stress on the sample with a stoichiometric Si3N4 passivation layer. The devices with additional sense node contacts enable the potential mapping between the gate and drain for ON-state and OFF-state, which helps to determine the distribution the charge trapping. By comparing the trap information extracted from the transient dynamic ON-resistance, the charge trapping appeared after the ON-state stress is proven to be associated with the deep buffer traps, likely due to the carbon acceptors in the GaN. Moreover, electroluminescence measurements show agreements with the potential mapping, and it also implies that the field plates possibly blocked the light emitted from the gate edge. RF AlGaN/GaN-on-SiC HEMTs are used for the breakdown study. The drain injected technique is used for avoiding device degradation while measuring the breakdown voltage as a function of the gate voltage. The drain current was kept as a constant while the gate voltage was swept during the measurements. The devices show a 2-stage breakdown feature as the first breakdown plateau is associated with the punch-through within the GaN channel layer under the gate, whereas the second breakdown plateau is due to the increasing carbon doping density as the punch-through current is forced down to the doped GaN layer. The electroluminescence results suggest that additional leakage paths are triggered with a high drain bias. Finally, a gate leakage study is carried out on the MIS AlGaN/GaN HEMTs. The bell-shape gate leakage curves for semi-ON state suggest the gate current is contributed by the electron current and hole current independently. The electrons mainly pass through the SiNx barrier by Poole-Frenkel emission whereas the hole current comes from the impact ionization. In addition, the peak shift of the bell shapes between the electroluminescence and the gate leakage indicates a potential competition mechanism.