Context of the tutorial: the IEEE CIS Summer School on Computational Intelligence and Applications (IEEE CIS SSoCIA 2022), associated with the 8th IEEE Latin American Conference on Computational Intelligence (IEEE LA-CCI 2022).; Doctoral; Random Neural Networks are a class of Neural Networks coming from Stochastic Processes and, in particular, from Queuing Models. They have some nice properties and they have reached good performances in several application areas. They are, in fact, queuing systems seen as Neural machines, and the two uses (probabilistic models for the performance evaluation of systems, or learning machines similar as the other more standard families of Neural Networks) refer to the same mathematical objects. They have the appealing that, as other special models that are unknown for most experts in Machine Learning, their testing in and/or adaptation to the many areas where standard Machine Learning techniques have obtained great successes is totally open.In the tutorial, we will introduce Random Neurons and the networks we can build with them, plus some details about the numerical techniques needed to learn with them. We will also underline the reasons that make them at least extremely interesting. We will also describe some of their successful applications, including our examples. We will focus on learning, but we will mention other uses of these models in performance evaluation, in the analysis of biological systems, and in optimization.