Neural Networks (NNs) with random weights represent nowadays a topic of consolidated use in the Machine Learning research community. In this contribution we focus in particular on recurrent NN models, which in a randomized setting represent a case of particular interest per se, entailing a number of intriguing research challenges primarily related to the control of the developed dynamics for the learning purposes. Framed in the Reservoir Computing paradigm, this paper aims at providing the basic elements and summarizing the recent advances on the topic of randomized recurrent NNs (divided in theoretical, architectural, deep learning and structured domain aspects), and introducing the papers accepted for the ESANN special session.