This paper studies problems related to visibility among points in the plane.
A point $x$ \emph{blocks} two points $v$ and $w$ if $x$ is in the interior of
the line segment $\bar{vw}$. A set of points $P$ is \emph{$k$-blocked} if each
point in $P$ is assigned one of $k$ colours, such that distinct points $v,w\in
P$ are assigned the same colour if and only if some other point in $P$ blocks
$v$ and $w$. The focus of this paper is the conjecture that each $k$-blocked
set has bounded size (as a function of $k$).