  Many problems in physics, material sciences, chemistry and biology can be
abstractly formulated as a system that navigates over a complex energy
landscape of high or infinite dimensions. Well-known examples include phase
transitions of condensed matter, conformational changes of biopolymers, and
chemical reactions. The energy landscape typically exhibits multiscale
features, giving rise to the multiscale nature of the dynamics. This is one of
the main challenges that we face in computational science. In this report, we
will review the recent work done by scientists from several disciplines on
probing such energy landscapes. Of particular interest is the analysis and
computation of transition pathways and transition rates between metastable
states. We will then present the string method that has proven to be very
effective for some truly complex systems in material science and chemistry.
