The nature of three-dimensional turbulent boundary layers (3DTBL) are discussed with the intention of applying them to the problems encountered in hydraulic engineering. After introducing the basic concepts of 3DTBL, various cross-flow and near-wall similarity models are described. A comparison between the flow situations commonly encountered in hydraulic engineering and in some other branches of fluid mechanics (which initially prompted the development of 3DTBL theories) is made to explore the possibilities of utilizing the 3DTBL theories in hydraulic engineering. There appears to be numerous opportunities to fruitfully apply 3DTBL theories in hydraulic engineering. One such application is presented in a companion paper.