I will explain how limiting configurations may be desingularized in order to obtain true solutions of Hitchin’s equation with large Higgs fields. This is joint work with Mazzeo, Swoboda and Witt. I will further discuss work in progress with the same authors directed at understanding the asymptotics of the complete Hyperkähler metric on the Higgs bundle moduli space, in particular the relation with the so-called semiflat metric. This is related to work of Gaiotto, Moore and Neitzke.