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Quantum mechanical effects of nuclei are ubiquitous in chemistry. For a typical example, zero-point energies and tunneling effects of the nuclei shift the chemical equilibrium and manipulate the reaction rate. However, theoretical investigation of such nuclear quantum effects in chemical reactions remains a challenge due to the heavy computation cost. To this end, imaginary-time path-integral based approximate methods have been previously introduced, which allows the inclusion of nuclear quantization in real-time chemical dynamics simulations at the efficiency of classical Newtonian dynamics. In the dissertation, we further extend the applicability of those path-integral methods and exploit the methods for practical chemical investigations. Specifically, we introduce novel dynamics approaches based on ring-polymer molecular dynamics methodology to incorporate nuclear quantum effects in the simulations of excited state dynamics and microcanonical scattering processes, and to examine the nuclear quantum effects in Hydrogen/Deuterium sticking to the graphene surface.