  Let $G$ be a connected graph. A vertex $w\in V(G)$ strongly resolves two
vertices $u,v\in V(G)$ if there exists some shortest $u-w$ path containing $v$
or some shortest $v-w$ path containing $u$. A set $S$ of vertices is a strong
metric generator for $G$ if every pair of vertices of $G$ is strongly resolved
by some vertex of $S$. The smallest cardinality of a strong metric generator
for $G$ is called the strong metric dimension of $G$. It is well known that the
problem of computing this invariant is NP-hard. In this paper we study the
problem of finding exact values or sharp bounds for the strong metric dimension
of strong product graphs and express these in terms of invariants of the factor
graphs.
