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We will review some of the state space, geometric and module theoretic results about observers, all within the standard system approach based on the input/output paradigm. In view of the rapid development of behavior theory, initiated by J.C. Willems, there is a clear need for the development of observer theory in the behavioral framework. A first and important step in this direction is the work of Valcher and Willems. The behavioral approach has certain advantages as far as observers are concerned. Elimination theory enables us to focus on the relation between the observed variables and the variables we want to estimate without necessarily going to full state modelling with a full state observer construction. We will explain the relation between classical observer theory and that of behavioral based. A principal tool is that of behavior homomorphisms introduced recently by the speaker.