Trapping phenomena are essential features controlling the transport properties of insulating materials. Depending on the energy depth, traps can either assist transport or lead to long-lasting storage of charges. The consequences of charge trapping are non-linear phenomena and electric field distribution distortion in the dielectric bulk. The important characteristics about traps are the nature of the levels, their depth in energy, and their density. In this review, we discuss the different techniques available to probe the energetics of traps, particularly in insulating polymers. The methods implemented for approaching the characteristics of traps range from atomistic simulation based on known physical/chemical defects, identification by spectroscopic techniques, and coupled opticalelectrical or thermal-electrical techniques. The review is focused on methods involving thermal or optical excitation coupled to detection using electrical or luminescence response with questioning about the physical hypotheses behind the analysis and the difference in response obtained through the various approaches. The technical implementation of these methods is described, along with examples of application. The differences in trap depth estimation from optical and thermal methods is discussed as well as the impact of having distributed trap depths. The input of luminescence techniques, which provide a fingerprint of chemical groups involved in charge recombination, is put forward.