The observations of long-lived surface nanobubbles in various experiments have presented a theoretical challenge, as they were supposed to be dissolved in microseconds owing to the high Laplace pressure. However, an increasing number of studies suggest that contact line pinning, together with certain levels of oversaturation, is responsible for the anomalous stability of surface nanobubbles. This mechanism can interpret most characteristics of surface nanobubbles. Here, we summarize recent theoretical and computational work to explain how the surface nanobubbles become stable with contact line pinning. Other related work devoted to understanding the unusual behaviors of pinned surface nanobubbles is also reviewed here.