Quantitative (or numerical) possibility theory offers a simple but yet very expressive setting for handling higher-order uncertainty and in particular imprecise probabilities. The paper surveys the basic ideas and notions underlying numerical possibility theory, its relation to the other uncertainty settings and its use in AI-related issues. Numerical possibility theory looks of interest for coping with imperfect statistical information, especially non-Bayesian statistics relying on likelihood functions and confidence intervals. Quantitative possibility theory can be used in inference, machine learning, tracking and information fusion, and finally preference modeling.