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The Division Theorem is the essential analytic instrument in the characterization of C^∞ stable proper mappings set up by J. Mather. Moreover, by using the Division Theorem one proves the Generalized Malgrange Preparation Theorem which is the most'important analytic and algebraic tool in the study of local singularities. Our purpose here is to gather the different statements and proofs of the Preparation Theorems and Division Theorems throughout the literature in a way made as complete as possible. Effort was taken in order to clarify and relate them, even recent versions of the Division Theorem on finitely differentiable maps such as those by M. G. Lassale, Pierre Milman, Edward Bierstone. Finally, the last chapter is concerned with some applications.