Ab initio quantum-chemical calulations with inclusion of electron correlation made since 1994 (such reliable calculations were not feasible before) significantly modified our view on interactions of nucleic acid bases. These calculations allowed to perform the first reliable comparison of the strength of stacked and hydrogen bonded pairs of nucleic acid bases, and to characterize the nature of the base-base interactions. Although hydrogen-bonded complexes of nucleobases are primarily stabilized by the electrostatic interaction, the dispersion attraction is also important. The stacked pairs are stabilized by dispersion attraction, however, the mutual orientation of stacked bases is determined rather by the electrostatic energy. Some popular theories of stacking were ruled out: The theory based on attractive interactions of polar exocyclic groups of bases with delocalized electrons of the aromatic rings (Bugg et al., Biopolymers 10, 175 (1971), and the pi-pi interactions model (C.A. Hunter, J. Mol. Biol. 230, 1025 (1993)). The calculations demonstrated that amino groups of nucleobases are very flexible and intrinsically nonplanar, allowing hydrogen-bond-like interactions which are oriented out of the plane of the nucleobase. Many H-bonded DNA base pairs are intrinsically nonplanar. Higher-level ab initio calculations provide a unique set of reliable and consistent data for parametrization and verification of empirical potentials. In this article, we present a short survey of the recent calculations, and discuss their significance and limitations. This summary is written for readers which are not experts in computational quantum chemistry.