To show that the Gamma function, restricted to the positive real half-axis, generates an o-minimal structure over the real field, we had to show (in collaboration with Lou van den Dries) that the expansion of the real field by all functions that are multisummable in the positive real direction is o-minimal. In the more recent context of the Pila-Wilkie estimates, this structure is receiving some renewed interest. I will summarize some of these new developments concerning multisummability and o-minimality.