  For a connected graph $G$ of order at least $2$ and $S\subseteq V(G)$, the
\emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size
among all connected subgraphs whose vertex sets contain $S$. In this paper, we
summarize the known results on the Steiner distance parameters, including
Steiner distance, Steiner diameter, Steiner center, Steiner median, Steiner
interval, Steiner distance hereditary graph, Steiner distance stable graph,
average Steiner distance, and Steiner Wiener index. It also contains some
conjectures and open problems for further studies.
