We review, under a historical perspective, the development of the problem of nonfundamentalness of Moving Average (MA) representations of economic models. Nonfundamentalness typically arises when agents’ information space is larger than the econometrician’s one. Therefore it is impossible for the latter to use standard econometric techniques, as Vector AutoRegression (VAR), to estimate economic models. We restate the conditions under which it is possible to invert an MA representation in order to get an ordinary VAR and identify the shocks, which in a VAR are fundamental by construction. By reviewing the work by Lippi and Reichlin [1993] we show that nonfundamental shocks may be very different from fundamental shocks. Therefore, nonfundamental representations should not be ruled out by assumption and indeed methods to detect nonfundamentalness have been recently proposed in the literature. Moreover, Structural VAR (SVAR) can be legitimately used for assessing the validity of Dynamic Stochastic General Equilibrium models only if the representation associated with the economic model is fundamental. Factor models can be an alternative to SVAR for validation purposes as they do not have to deal with the problem of nonfundamentalness.