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It is the purpose of the present contribution to demonstrate that thegeneralization of the concept of a quantum mechanical observable from theHermitian operator of standard quantum mechanics to a positive operator-valuedmeasure is not a peripheral issue, allegedly to be understood in terms of atrivial nonideality of practical measurement procedures, but that thisgeneralization touches the very core of quantum mechanics, viz. complementarityand violation of the Bell inequalities.Comment: Contribution to Proceedings of the Workshop `Beyond the quantum',  Leiden, May/June 200

POVMs: A SMALL BUT IMPORTANT STEP BEYOND STANDARD QUANTUM MECHANICS