This chapter proposes a novel general stochastic formulation for the Life-Cycle Analysis (LCA) of deteriorating engineering systems. The formulation rigorously formalizes the different aspects of the life-cycle of engineering systems. To capture the probabilistic nature of the proposed formulation, it is named Stochastic Life-Cycle Analysis (SLCA). The life-cycle of an engineering system is shaped by deterioration processes and repair/recovery processes, both characterized by several sources of uncertainty. The deterioration might be due to exposure to environmental conditions and to both routine and extreme loading. The repair and recovery strategies are typically implemented to restore or enhance the safety and functionality of the engineering system. In the SLCA, state-dependent stochastic models are proposed to capture the impact of deterioration processes and repair/recovery strategies on the engineering systems in terms of performance measures like instantaneous reliability and resilience. The formulation integrates the state-dependent stochastic models with the previously developed Renewal Theory-based Life-Cycle Analysis (RTLCA) to efficiently evaluate additional system performance measures such as availability, operation cost, and benefits. The proposed SLCA can be used for the optimization of the initial design and mitigation strategies of engineering systems accounting for their life-cycle performance. As an illustration, the proposed SLCA is used to model the life-cycle of a reinforced concrete bridge, subject to deteriorations caused by corrosion and earthquake excitations. The deteriorated bridge column is repaired using Fiber Reinforced Polymer (FRP) composites. The results show that the deterioration processes significantly affect the performance measures of the example bridge.