We first provide a historical account of how interdisciplinary research was done over the ages, up to relatively recent times during which interdisciplinary research became moribund. We then focus on even more recent times during which, because of genuine interest or for more mundane reasons, multidisciplinary research has come into vogue. We also discuss the shortcomings of these latter efforts. We then focus on computational science and engineering and, in particular, how interdisciplinary research should be effected, and more important, how current and future generations of computational scientists and engineers should be trained.