I discuss the problem whether certain Cayley graphs form an expander family. A family of graphs is called an expander family, if the number of edges needed to be deleted from any of the graphs to make it disconnected is at least a constant multiple of the size of the smallest component we get. Let $S$ be a subset of $SL(d, Z)$ closed for taking inverses. For each square-free integer $q$ consider the graph whose vertex-set is $SL(d, Z/qZ)$ two of which is connected by an edge precisely if we can get one from the other by left multiplication by an element of $S$. Bourgain, Gamburd and Sarnak proves that if $d=2$ and $S$ generates a Zariski dense subgroup of $SL2$, then these graphs form an expander family. In the talk I outline a modification of their argument which leads to a simpler proof and allows a generalization to $d=3$ or to general number fields.