In the present paper we review the most recent degradation modes and mechanisms recently observed in AlGaN/GaN (Aluminum Gallium Nitride/Gallium Nitride). High Electron-Mobility Transistors (HEMTs), as resulting from a detailed accelerated testing campaign, based on reverse bias tests and DC accelerated life tests at various temperatures. Despite the large efforts spent in the last few years, and the progress in mean time to failure values, reliability of GaN HEMTs, and millimeter microwave integrated circuits still represent a relevant issue for the market penetration of these devices. The role of temperature in promoting GaN HEMT failure is controversial, and the accelerating degradation factors are largely unknown. The present paper proposes a methodology for the analysis of failure modes and mechanisms of GaN HEMTs, based on (i) DC and RF stress tests accompanied by an (ii) extensive characterization of traps using deep level transient spectroscopy and pulsed measurements, (iii) detailed analysis of electrical characteristics, and (iv) comparison with two-dimensional device simulations. Results of failure analysis using various microscopy and spectroscopy techniques are presented and failure mechanisms observed at the high electric field values typical of the operation of these devices are reviewed.