Leptoquarks are theoretically well-motivated and have received increasing attention in recent years as they can explain several hints for physics beyond the Standard Model. In this article, we calculate the renormalisation group evolution of models with scalar leptoquarks. We compute the anomalous dimensions for all couplings (gauge, Yukawa, Higgs and leptoquarks interactions) of the most general Lagrangian at the two-loop level and the corresponding threshold corrections at one-loop. The most relevant analytic results are presented in the appendix, while the notebook containing the full expressions can be downloaded at https://github.com/SumitBanikGit/SLQ-RG. In our phenomenological analysis, we consider some exemplary cases with focus on gauge and Yukawa coupling unification.