We revisit scalar leptoquark pair-production at hadron colliders and significantly improve the level of precision of the cross section calculations. Apart from QCD contributions, we include lepton t-channel exchange diagrams that turn out to be relevant in the light of the recent B-anomalies. We evaluate all contributions at next-to-leading-order accuracy in QCD and resum, in the threshold regime, soft-gluon radiation at next-to-next-to-leading logarithmic accuracy. Our predictions consist hence in the most precise leptoquark cross section calculations available to date, and are necessary for the best exploitation of leptoquark searches at the LHC.