We are currently in the ``data'' age. As we enter the ``information'' age the problem of learning functional relationships from data will loom large. We provide an assessment of results ranging from perceptrons and neural networks to function estimation in general.

In recent years, progress has been made on the function theoretic basis of approximation methods. Progress has also been made on the problem of learning from data.

Two main difficulties center around (i) assessment of the function class in which the true function is assumed to exist, and (ii) the existence of a computationally tractable algorithm for assimilating the training data.

We show that there do exist finite algorithms for training; however the required computational complexity can be very high. We also show that the formulation of the training problem as a convex optimization problem presents some difficulties, at least if approached in a straightforward fashion.

Finally almost no work has been done, to our knowledge, on the capability of the function estimation methods to solve high level problems of interest, as was done for example in the case of perceptrons.