This thesis is concerned with the specification, estimation, application and testing of stochastic frontier production functions. The majority of the material in this document is derived from seven research papers written over the past four years. The thesis begins with a review of frontier estimation methods, with an emphasis on information relevant to agricultural applications. The two primary methods of frontier estimation, stochastic frontiers and data envelopment analysis (DEA), are described and compared. The influence of data noise is observed to be crucial in the selection of appropriate methods.