Many Ge and III-V-based MOSFETs as well as GaN-based HEMTs and MOS-HEMTs are significantly compromised in performance and reliability by their high densities of interface, border, and bulk oxide traps. Problems may also arise when characterizing traps in FETs made on modern high mobility channels, due to their device structures and material properties that are different from their conventional counterparts. In this talk, we present the results of our study of these traps as obtained by the use of several electrical characterization techniques. In particular, we will review the novel ac transconductance technique that we recently introduced, which enables us to probe interface traps in the band gap as well as border and bulk traps in the gate dielectrics even without a body contact. We will also show that the Inelastic Electron Tunneling Spectroscopy (IETS) offers the unique capability to provide spatial and energy information about traps, as well as to distinguish between two types of traps: those that give rise to trap-assisted conduction and those that simply trap carriers. Ionizing radiation-induced trapping of charges in MOS-FETs and MOS-HEMTs made on III-V semiconductors are also reported and discussed.