We start by presenting the production optimization problem in oil and gas production and also add some comments to the closely linked reservoir optimization problem. Subsequently, a non-invasive optimization approach is presented prior to concepts that apply decomposition and structure exploitation. This includes splitting a network simulator into interconnected parts to exploit couplings in devising efficient formulations and algorithms. Further, we discuss reservoir optimization where there is no apparent structure to exploit. However, by recognizing this as a dynamic optimization problem, it may be partitioned in the time domain. The presentation includes results based on data from real assets, including economic benefits.