This thesis proposes a systematic Bayesian approach for uncertainty quantification with an application for petroleum reservoirs. First, we demonstrated the potential of additional misfit functions based on specific events in reservoir management, to gain knowledge about reservoir behaviour and quality in probabilistic forecasting. Water breakthrough and productivity deviation were selected and provided insights of discontinuities in simulation data when compared to the use of traditional misfit functions (e.g. production rate, BHP) alone. Second, we designed and implemented a systematic methodology for uncertainty reduction combining reservoir simulation and emulation techniques under the Bayesian History Matching for Uncertainty Reduction (BHMUR) approach. Flexibility, repeatability and scalability are the main features of this high-level structure, incorporating innovations such as phases of evaluation and multiple emulation techniques. This workflow potentially turns the practice of BHMUR more standardised across applications. It was applied for a complex case study, with 26 uncertainties, outputs from 25 wells and 11+ years of historical data based on a hypothetical reality, resulting in the construction of 115 valid emulators and a small fraction of the original search space appropriately considered non-implausible by the end of the uncertainty reduction process. Third, we expanded methodologies for critical steps in the BHMUR practice: (1) extension of statistical formulation to two-class emulators; (2) efficient selection of a combination of outputs to emulate; (3) validation of emulators based on multiple criteria; and (4) accounting for systematic and random errors in observed data. Finally, a critical step in the BHMUR approach is the quantification of model discrepancy which accounts for imperfect models aiming to represent a real physical system. We proposed a methodology to quantify the model discrepancy originated from errors in target data that are set as boundary conditions in a numerical simulator. Its application demonstrated that model discrepancy is dependent on both time and location in the input space, which is a central finding to guide the BHMUR practice in case of studies based on real fields.