The idea is to shift focus from the measure-theoretic details to structural properties of information flow in the presence of uncertainty - independence, conditioning, nested uncertainty, etc. This shift allows one to reason without the need to specify a concrete model of uncertainty, be it discrete, continuous, Gaussian, possibilistic or one of many other instantiations. In this talk, I will present a high-level overview of the leading approach to categorical probability that is based on so-called Markov categories. We will focus on the diagrammatic language of Markov categories that can be understood without any knowledge of category theory. Using such diagrams, we can also express basic concepts that have been useful in proving a plethora of categorical versions of classical theorems - strong law of large numbers, de Finetti's theorem, d-separation criterion for Bayesian networks, ergodic decomposition theorem, zero/one laws and others.