Given the prevalence of statistical techniques that use probability to quantify uncertainty, the aim of this article is to highlight the theoretical aspects and implications of the major current probability interpretations that justify the development and use of such techniques. After briefly sketching the origins and development of the notion of probability, its theoretical interpretations will be outlined. Two main trends will be distinguished: one epistemic and one empirical, cor-responding to the twofold meaning characterizing probability. The epistemic type embodies the so-called classical theory put forward by Laplace as well as the logical and subjective approaches. By contrast, the frequency and propensity theories are, in theory, e...