The continuous size downscaling of complementary metal-oxide-semiconductor (CMOS) transistors has led to the replacement of SiO2 with a HfO2-based high dielectric constant (or high-k) oxide, and the polysilicon electrode with a metal gate. The approach to this technological evolution has spurred a plethora of fundamental research to address several pressing issues. This review focusses on the large body of first principles (or ab initio) computational work employing conventional density functional theory (DFT) and beyond-DFT calculations pertaining to HfO2-based dielectric stacks. Specifically, structural, thermodynamic, electronic, and point-defect properties of bulk HfO2, Si/HfO2 interfaces, and metal/HfO2 interfaces are covered in detail. Interfaces between HfO2 and substrates with high mobility such as Ge and GaAs are also briefly reviewed. In sum, first principles studies have provided important insights and guidances to the CMOS research community and are expected to play an even more important role in the future with the further optimization and "scaling down" of transistors.