This text examines the various ways in which prisms and small mirrors typically are designed and mounted in optical instruments. It provides analytical tools for evaluating different designs, and discusses the advantages and disadvantages of various techniques. The book, in part, is an outgrowth of SPIE short courses taught by the author and is a companion to his 1995 volume "Mounting Lenses in Optical Instruments". The work should be useful for engineers and other practitioners in the fields of optical engineering and optomechanical design.