There has been a long debate among economists whether it is more reasonable to think that firms choose prices as strategic variables or quantities. A firm may not want to commit to one of these simple types of strategies if uncertainty is introduced since there may be decisions which must possibly be made in advance and can not be made after the resolution of the uncertainty. The supply function, which is implicitly determined by these decisions, relates the quantity a firm will produce to the price the market will create. This book analyzes the behaviour of firms in a world of uncertainty on a basis of three famous contributions to the topic "supply functions". It is shown that choosing a supply function is superior to standard approaches since firms are able to react in a better way to changing market conditions compared to a situation where price or quantity is fixed, as stipulated by Bertrand or Cournot competition, respectively. The theoretical approaches of these supply function models are finally linked to applications to electricity markets. It is also analyzed if the concept of supply function equilibria is valid in reality.