High-κ dielectrics are insulating materials with higher permittivity than silicon dioxide. These materials have already found application in microelectronics, mainly as gate insulators or passivating layers for silicon (Si) technology. However, since the last decade, the post-Si era began with the pervasive introduction of wide band gap (WBG) semiconductors, such as silicon carbide (SiC) and gallium nitride (GaN), which opened new perspectives for high-κ materials in these emerging technologies. In this context, aluminium and hafnium oxides (i.e., Al2O3, HfO2) and some rare earth oxides (e.g., CeO2, Gd2O3, Sc2O3) are promising high-κ binary oxides that can find application as gate dielectric layers in the next generation of high-power and high-frequency transistors based on SiC and GaN. This review paper gives a general overview of high-permittivity binary oxides thin films for post-Si electronic devices. In particular, focus is placed on high-κ binary oxides grown by atomic layer deposition on WBG semiconductors (silicon carbide and gallium nitride), as either amorphous or crystalline films. The impacts of deposition modes and pre- or postdeposition treatments are both discussed. Moreover, the dielectric behaviour of these films is also presented, and some examples of high-κ binary oxides applied to SiC and GaN transistors are reported. The potential advantages and the current limitations of these technologies are highlighted.