  The steep increase of the relaxation time of glass forming liquids upon
cooling is traditionally ascribed to an impending entropy crisis: since the
system has "nowhere to go", dynamics must come to a halt. This classic
argument, due to Adam \& Gibbs, has been bolstered and refined by the
development of the Random First Order Transition (RFOT) theory, which fares
remarkably well at reproducing most salient experimental facts of super-cooled
liquids. All static predictions of RFOT, including the existence of a
point-to-set length and the role of pinning sites, have been vindicated by
detailed numerical simulations. Yet, there is no consensus that the basic
mechanism explaining the glass transition is the one captured by RFOT. Strong
doubts have emerged following the observation that adding or removing kinetic
constraints can change the relaxation time by orders of magnitude, while
leaving thermodynamics unchanged. This is at odds with the idea of a one-to-one
mapping between excess entropy and relaxation time.
  In the following discussion paper presented at the Solvay conference in
October 2023, we review areas of consensus and dissent of RFOT with other
competing theoretical proposals, and propose possible paths for (partial)
reconciliation. We further argue that extensive numerical simulations of the
non-linear susceptibility of glasses, in particular in the aging regime, should
shed important light on the mechanism at the origin of the super-Arrhenius
behaviour of the relaxation time. In any case, more imagination is still needed
to come up with experimental, theoretical or numerical ideas that would allow
to finally settle the question of why glasses do not flow.
