In this talk, we introduce some rogue wave phenomena,causesofoccurrenceand their dynamic behaviors. We present some efficient and accurate numerical experiments to simulate the vector rogue waves of the coupled nonlinear Schrödinger equations with the coherent coupling effect. A small computation interval of errors is considered to efficiently simulate rogue waves and compare different numerical methods. The vector rogue-wave solutions are always unstable under small perturbations, while such rogue wave dynamics may have a certain degree of stability that it has potential to be observed in experiments.