We discuss how strong lensing by galaxy clusters may be used to study the properties of dark matter halos and the expansion history of the universe. First, we show how the characteristics of $\Lambda$CDM clusters determine their lensing properties, and show how these properties are manifested in some of the new giant arcs discovered behind SDSS clusters. Next, we compare the statistics of strong lensing by clusters expected in the $\Lambda$CDM model to the observed statistics of giant arcs and wide-separation quasars. Finally, we discuss the cosmographic uses of clusters with multiple arcs, pointing out several sources of noise which can produce $\gtrsim100$ % errors in derived cosmological parameters.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html