The study of deep level defects in semiconductors has always played a strategic role for the development of electronic and optoelectronic devices. In fact, deep levels have a strong impact on many of the device properties, including the efficiency, stability, and reliability because they can drive several physical process. Despite the advancements in crystal growth, wide and ultrawide bandgap semiconductors (such as gallium nitride and gallium oxide) are still strongly affected by the formation of defects that in general can act as carrier traps or generation-recombination centers. Conventional techniques used for deep level analysis in silicon need to be adapted for identifying and characterizing defects in wide bandap materials. This topical review paper presents an overview of reviews the theory of deep levels in semiconductor; in addition, we present a review and original results and on the application, limits and perspectives of two widely adopted most common deep -levels detection techniques, namely capacitance deep level transient spectroscopy and deep level optical spectroscopy, with specific focus on wide bandgap semiconductors. Finally, the most common traps of GaN and β-Ga2O3 are reviewed.