The thesis mainly concentrate on developing new methodologies and numerical techniques to reveal quantum effects in chemical dynamics. It contains two topics in this field.One is involved in the forward-backward semiclassical dynamics. Within a differential expression of the Heisenberg operator, the forward and backward evolution can be joined along the closed time contour. This leads to a dramatic cancellation of oscillation due to the two individual propagators in the Heisenberg operator and the resulting forward-backward propagator is free of the expensive evaluation prefactor and thus more tractable to semiclassical approximations. This approach provides a general means to obtain different prefactor-free semiclassical propagators from different initial value representations. Numerical calculation shows that they are also capable of describing quantum dynamics semiquantitatively and the accuracies are similar with the classical Wigner method.The other is concerned with the stochastic description of the dissipative dynamics. Based on the Hubbard-Stratonovich transformation, the dissipative interaction between the system of interest and the heat bath is decoupled and the separated system and the bath thus evolve in the common virtually stochastic field. This manipulation allows us to establish a novel theoretical methodology by which the reduced density matrix is formulated as anensemble average of its random realizations. For the Caldeira-Leggett model, a deterministic hierarchy as well as a mixed random-deterministic approach is established to obtain the reduced density matrix. These procedures are successfully applied to study the quantum dynamics of the two-level system and the results display that the current approaches are highly efficient.