I will discuss certain remarkable q-difference equations with regular singularities that appear in enumerative K-theory and representation theory. This class includes, in particular, the quantum Knizhnik-Zamolodchikov equations of Frenkel and Reshetikhin. Remarkably, the geometric origin of these equations helps with the computations of the monodromy, as shown in our join work with Mina Aganagic.