It has been 30+ years since the discovery of the top quark, the heaviest elementary particles known to date, yet its studies continue to be one of the most important scientific activities within the LHC programme. The physics of the top quark plays a crucial role for our understanding of the Standard Model, searches for possible new physics and, as of late, provides a new way to study quantum-mechanical phenomena such as entanglement. In this talk, I will review recent theoretical progress in precision computations of top-quark production at the LHC.