Abstract: Let $P$ be a set of $n$ points in the plane.
Two points $p_i$ and $p_j$ of $P$ are \emph{mutually visible} if
the line segment $p_ip_j$ does not contain or pass through any other point
of $P$. The {\it visibility graph} (also called the {\it point visibility graph}) $G$
of $P$ is defined by associating a vertex $v_i$ with each point $p_i$ of $P$
such that $(v_i, v_j)$ is an undirected edge of $G$ if $p_i$ and $p_j$
are mutually visible.

In this review talk, we present open problems and conjectures on
visibility graphs of points for graph-theoretic problems along with necessary
backgrounds for understanding them.