  A set of $n$ points in the Euclidean plane determines at least $n$ distinct
lines unless these $n$ points are collinear. In 2006, Chen and Chv\'atal asked
whether the same statement holds true in general metric spaces, where the line
determined by points $x$ and $y$ is defined as the set consisting of $x$, $y$,
and all points $z$ such that one of the three points $x,y,z$ lies between the
other two. The conjecture that it does hold true remains unresolved even in the
special case where the metric space arises from a connected undirected graph
with unit lengths assigned to edges. We trace its curriculum vitae and point
out twenty-nine related open problems plus three additional conjectures.
