This paper provides an overview of the literature on production under the influence of risk. Various specifications of stochastic production function such as models with additive and multiplicative uncertainty, Just and Pope model, output-cubical, stateallocable and state-general models are discussed. Further, criteria determining optimal producer behaviour are derived for deterministic production technology and for various kinds of state-contingent technologies such as output-cubical, state-specific, stateallocable and state-general technologies. Finally, a brief discussion is presented about the drawbacks of each of these specifications of technology.