  The idea that a thermodynamic glass transition of some sort underlies the
observed glass formation has been highly debated since Kauzmann first stressed
the hypothetical entropy crisis that could take place if one were able to
equilibrate supercooled liquids below the experimental glass transition
temperature $T_g$. This a priori unreachable transition at some $T_K<T_g$ has
since received a firm theoretical basis as a key feature predicted by the
mean-field theory of the glass transition. In this chapter, we assess whether,
and in which form, such a transition can survive in finite dimensions, and we
review some of the recent computer simulation work addressing the issue in $2$-
and $3$-dimensional glass-forming liquid models. We also discuss theoretical
reasons to focus on an apparently inaccessible singularity.
