The counting theorem of Pila and Wilkie opened up one of the most important developments in model theory in recent years. It provides a bound on the density of rational points for sets definable in o-minimal expansions of the real field, a result which has had several stunning number-theoretic applications (e.g. to the Manin-Mumford and André-Oort Conjectures). Central to the proof of the theorem is an o-minimal version of Yomdin-Gromov parameterization, a tool which was originally introduced in the 1980s for studying topological entropy and volume growth in smooth dynamics. The idea of this technique (and other related notions of ``smooth parameterization'') is to decompose sets using functions with controlled higher-order derivatives, resulting in various geometrical and arithmetical consequences. We will provide some background on various applications of smooth parameterizations, and, time permitting, discuss different aspects of ongoing work to improve them. One direction is the pursuit of an effective version of the Pila--Wilkie Counting Theorem, which we have begun by establishing such a result for certain surfaces described by restricted Pfaffian functions, making use of the work of Khovanskii, Gabrielov and Vorobjov. Another direction is the study of ``mild parameterization'', a type of smooth parameterization, in o-minimal structures. This is aimed towards a conjecture of Wilkie, which proposes a significant sharpening of the Pila--Wilkie bound for sets definable in the (o-minimal) real exponential field, to approach which mild parameterization has been the main geometric tool used to date.