The purpose of the talk is to provide a gentle and informal introduction to a recent monograph written jointly with Nicolas Curien and Armand Riera on self-similar Markov trees. These form a remarkable family of random compact real trees further endowed with a decoration function and a natural finite measure; as the terminology suggests, they are self-similar objects that further satisfy a Markov branching property.
Self-similar Markov trees arise as the scaling limits of a great variety of Galton-Watson processes with integer types. They encompass many random real trees that have been studied over the last decades, such as the Brownian CRT, stable Lévy trees, fragmentation trees, and growth-fragmentation trees.