Band-crossing is a quantum dynamical behavior that contributes to important physics and chemistry phenomena such as quantum tunneling, Berry co nnection, chemical reaction etc. In this talk, we will discuss several recent works in developing semiclassical methods for band-crossing, including examples from surface hopping, Schrodinger equation with periodic potentials, and high frequency solutions of linear hyperbolic systems with polarized waves. For such systems we will also introduce an "asymptotic-preserving" method that is accurate uniformly for all wave numbers.