This review covers the synthesis, characterization, and physico-chemical properties of microporous and mesoporous aluminophosphates and silicoaluminophosphates molecular sieves. Particular emphasis is given to the materials that have found applications as acid catalysts. We consider the evolution of the synthesis procedures from the first discoveries to the current methodologies and give perspectives for new possible synthesis strategies. Emphasis is given to the use of specially prepared precursors/reactants designed for the use as molecular sieves. Experimental (especially MAS-NMR and FTIR spectroscopy) and theoretical approaches to the description of the Si insertion into the ALPO framework and to the acidic properties of SAPOs and MeAPSOs materials are discussed. Copyright © 2005 by Annual Reviews. 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