An accurate description and understanding of matter clustering in the strongly non-linear regime, even neglecting baryonic effects, remains a problem which is relevant to cosmology and of fundamental interest. My talk will be structured around three questions about it: (1) How well do current simulations resolve this clustering? (2) Is the so-called "stable clustering" approximation a relevant one? (3) Are there really "universal" properties of non-linear clustering? I will report results addressing these questions using mostly simulations of so-called "scale-free" cosmological models. They both show that these questions are closely linked to one another, and provide some answers which future studies of this kind should be able to refine.