Abstract: The dynamics of complex biological systems is often driven by multiscale, rare but important events. In this talk, I will first introduce the numerical methods for computing transition states, in particular, the Optimization-based Shrinking Dimer (OSD) method we recently proposed. Then I will give two applications of rare events and transition states in biology: boundary sharpening in zebrafish hindbrain and neuroblast delamination in Drosophila. The joint work with Qiang Du (Columbia), Qing Nie (UC Irvine), Yan Yan (HKUST).