Whenever there are observed dynamic data obtained from the reservoir understudy, we can reduce the geological uncertainty by conditioning the prior geological realizations to the observed data (Oliver and Chen in Computational Geosciences. 15:185–221, 2010; Ghoniem et al. in Applied Mathematical Modelling. 8:282–287, 1984; Heidari et al. in Computers and Geosciences. 55:84–95, 2013;Zhang and Oliver in SPE Journal. 16:307–317, 2011). This kind of uncertainty management is an inverse uncertainty management/quantification, which is mainly based on Bayesian approaches as described in Sect. 1.5.2. Inverse uncertainty management is technically known as model updating, model conditioning, model adjusting, model calibration, parameter estimation, data assimilation, history matching, automated history matching, or computer-assisted history matching. No matter what you call this process, it helps to have better and more reliable estimations of the true model. This chapter provides the details of history matching, different data types and their scale that are used in history matching, use of seismic, static, and production data in history matching, challenges encountered during history matching, history matching methods, and different approaches to reservoir management under geological uncertainty. Open-loop and closed-loop reservoir management are described and their pros and cons are discussed. Also, the most commonly used ensemble-based methods, ensemble-smoother methods, and stochastic optimization algorithms used for history matching are described.