Stochastic context free grammars are a formalism which plays a prominent role in RNA secondary structure analysis. This chapter provides the theoretical background on stochastic context free grammars. We recall the general definitions and study the basic properties, virtues, and shortcomings of stochastic context free grammars. We then introduce two ways in which they are used in RNA secondary structure analysis, secondary structure prediction and RNA family modeling. This prepares for the discussion of applications of stochastic context free grammars in the chapters on RFAM (6), Pfold (8), and INFERNAL (9).