The choice under uncertainty is treated in economics by different approaches. We can distinguish three of them, two of which concern individual choice, while the third frames individual choices within the analysis of the social system. The differences between these derive from the diversity of the questions to which they intend to respond. The first approach asks how a rational decision-maker must choose; the second one how a real decision-maker behaves; and the third one how decision-makers can be represented in the general economic theory without specific assumptions on their preferences under uncertainty. The main theories that result from these approaches are briefly presented. They are, according to the first approach, the Expected Utility theory (in the two axiomatic versions provided by von Neumann and Morgenstern and by Savage) and the theories of Rank Dependent Expected Utility and Choquet Expected Utility. Following the second approach, the Prospect Theory is indicated. Taking under consideration the third approach, it is remarked that the analysis included in the modern presentation of general equilibrium theory (for example, that provided by Debreu) does not present peculiar characteristics and, thus, provides a general reference to the analysis of the choice under uncertainty. The main features that distinguish the different theories and that make them, in part, similar are highlighted. The indifference maps obtained by following the three approaches in case of only two possible events are compared. It is, finally, discussed the relationship between subjective probability and the reservation prices of the acts related to the events and the reference to the Dutch book argument.