The geometric tool of parameterization has important diophantine consequences, was central to the proof of the Pila-Wilkie Theorem and remains the key approach in the ongoing pursuit of further applications of o-minimality to number theory. In this talk I will discuss a number of results which help improve our understanding of certain types of parameterization in the o-minimal setting, focussing in particular on questions of their definability and effectivity. (Variously work with Derya Çıray and with Gareth Jones.)