When the preferences of a consumer can be represented by a utility function, the consumption (the demand) of the consumer is obtained by the maximization of the utility under the consumer budget constraint and the prices of goods. Actually, what is known is the demand correspondence obtained from observations and not one hypothetical utility function. The revealed preferences consists in constructing utility functions from demand correspondences. We present a short state of art on the question in the differentiable case as well in the non differentiable case. Things are not so simple as shown from some pathological examples.