Abstract: Developing an accurate and practical method for computing chemical reaction rates is one of the fundamental subjects of theoretical chemistry. Within the Born-Oppenheimer approximation, a rigorous calculation needs one to solve the dynamics for nuclear motion on the appropriate Born-Oppenheimer potential energy surface. There are various approximate ways for treating the nuclear dynamics. In this regard; the most successful approach is probably the classical transition-state theory which has been applied widely to numerous reactions including biological systems and condensed phase systems. The fundamental assumption of transition-state theory is usually valid at not-too high temperature or for large dimensional systems. However, there is one inherent deficiency of the theory in that it is not able to account for quantum effects, which is usually non-negligible in low-temperature or light-atom transfer reactions. Therefore, a quantum correction factor needs to be calculated in a posteriori manner. The alternative approach is to develop an approximated quantized transition-state theory by starting from the rigorous quantum rate expression with some approximations for neglecting recrossing effects. The recently developed quantum instanton (QI) model belongs to the category of quantum transition-state theory for calculating thermal rate constants of chemical reactions. The QI model has been shown with a considerable promise as a general and accurate method for calculating rate constants for reactions in complex molecular systems. To apply quantum instanton model to complex systems, path-integral Monte-Carlo simulations need to be done. Much progress and numerical improvement as well as design of new path-integral estimators have been done successfully to ensure the applicability of quantum instanton model to complex condensed phase systems.