  Arc statistics is known to be a powerful cosmological tool. Numerical lensing
simulations show that orders of magnitude differences in the number of {\em
giant} arcs on the whole sky are expected in different cosmological models. In
this paper, we discuss the analytic and numerical methods in arc statistics and
show that analytic models fail to reproduce the efficiency for strong lensing
of more realistic numerical cluster models. Then, we discuss two recent
extensions of the lensing simulations, i.e. the effects of cD galaxies in the
lensing clusters and the impact of cluster mergers on arc statistics. We show
that cD galaxies can increase the lensing cross sections for long and thin arcs
by perhaps up to $\sim50%$, while major mergers can change the cluster
efficiency for producing such arcs by up to one order of magnitude.

Astrophysics