Decision-making based on machine learning systems, especially when this decision-making can affect human lives, is a subject of maximum interest in the Machine Learning community. It is, therefore, necessary to equip these systems with a means of estimating uncertainty in the predictions they emit in order to help practitioners make more informed decisions. In the present work, we introduce the topic of uncertainty estimation, and we analyze the peculiarities of such estimation when applied to classification systems. We analyze different methods that have been designed to provide classification systems based on deep learning with mechanisms for measuring the uncertainty of their predictions. We will take a look at how this uncertainty can be modeled and measured using different approaches, as well as practical considerations of different applications of uncertainty. Moreover, we review some of the properties that should be borne in mind when developing such metrics. All in all, the present survey aims at providing a pragmatic overview of the estimation of uncertainty in classification systems that can be very useful for both academic research and deep learning practitioners.