The Random Neural Network Model has been introduced to model that apparently probabilistic and spiked behaviour of many natural neuronal assemblies. We will first summarise the model and its main mathematical and algorithmic properties. Specifically we will detail its product form solution, and present its O(n^3) learning algorithm. Then we will describe applications to modeling natural cortico-thalamic oscillations, and to texture based detailed recognition for anomaly detection in MRI images of the brain. We will concluding by describing how very similar models can also be used to represent the dynamics and equilibrium of gene regulatory networks. The talk will be based on papers that we have published in the journals Neural Computation, BioSystems, Proceedings IEEE, IEEE Trans. on Neural Networks, and the Physical Review E.