The theory of (double) affine Hecke algebras leads to two integrable structures: the commuting family of Macdonald-Ruijsenaars difference operators, and Cherednik's quantum affine Knizhnik-Zamolodchikov (KZ) equations. These two integrable structures are related through the difference Cherednik-Matsuo correspondence. A basis of solutions of the pertinent systems of equations can be constructed using asymptotic analysis. It leads to Harish-Chandra type series solutions, with the series expansions depending on a particular choice of Weyl chamber. The connection problem is the problem of explicitly computing the relation between the Harish-Chandra type solutions for neighbouring Weyl chambers. I will discuss the solution of the connection problem and its applications.