Pressure is an important thermodynamic parameter, allowing the increase of matter density by reducing interatomic distances that result in a change of interatomic interactions. In this context, the long range in which pressure can be changed (over six orders of magnitude with respect to room pressure) may induce structural changes at a much larger extent than those found by changing temperature or chemical composition. In this article, we review the pressure-induced phase transitions of most sesquioxides, i.e., A2O3 compounds. Sesquioxides constitute a big subfamily of ABO3 compounds, due to their large diversity of chemical compositions. They are very important for Earth and Materials Sciences, thanks to their presence in our planet’s crust and mantle, and their wide variety of technological applications. Recent discoveries, hot spots, controversial questions, and future directions of research are highlighted.