  A routing $R$ of a given connected graph $G$ of order $n$ is a collection of
$n(n-1)$ simple paths connecting every ordered pair of vertices of $G$. The
vertex-forwarding index $\xi(G,R)$ of $G$ with respect to $R$ is defined as the
maximum number of paths in $R$ passing through any vertex of $G$. The
vertex-forwarding index $\xi(G)$ of $G$ is defined as the minimum $\xi(G,R)$
over all routing $R$'s of $G$. Similarly, the edge-forwarding index $ \pi(G,R)$
of $G$ with respect to $R$ is the maximum number of paths in $R$ passing
through any edge of $G$. The edge-forwarding index $\pi(G)$ of $G$ is the
minimum $\pi(G,R)$ over all routing $R$'s of $G$. The vertex-forwarding index
or the edge-forwarding index corresponds to the maximum load of the graph.
Therefore, it is important to find routings minimizing these indices and thus
has received much research attention in the past ten years and more. In this
paper we survey some known results on these forwarding indices, further
research problems and several conjectures.
