The last decades have seen an expanding competition and complexity in the emerging energy markets, mainly due to the increasing deregulation and privatization of these markets. As a consequence, the dynamics of energy prices have become highly volatile and so energy traders are calling for new instruments and techniques in order to protect their exposures against the risks entailed by the energy markets. A key issue in the energy markets is the fact that energy (in particular oil and gas) can be stored physically. Such storage facilities allow for anticipating and exploiting market fluctuations of energy prices according to the principle “sell high” and “buy low”. Initially, storage facilities were only accessible by major players in the respective industries, who had sufficient capital to build and maintain them. Meanwhile, due to the emerging liberalization of the energy markets all participants have the possibility to trade storage services via storage exchange platforms. As a consequence on the one hand, design of optimal strategies involving buying, storing, and selling energy over time are called for. On the other hand, this resulted in a high demand of proper statistical prediction algorithms based on adequate statistical modeling of energy prices and storage markets. This whole development has further led to the appearance of structured contracts, also called energy derivatives. In the gas and energy markets for example, so called “swing options” have become very popular. An example swing option gives the holder the right to buy or sell a certain amount of gas, electricity or storage capacity at a certain prescribed number of trading dates. Energy derivatives are typically difficult to treat from a quantitative point of view due to their complex structured exercise features and their highly path-dependent structure. As a general consequence, the rising complexity of the markets poses a bunch of challenging mathematical issues that are to be resolved. These issues may be categorized into the following main streams: