Multielectrode recordings have revealed complex and coordinated population activity in neuronal networks. Among the variety of reported patterns, a central regime of synchronous activity is thought to serve important function and the disruptions of which could be associated to serious condition. A more debated regime is concerned with the distribution of avalanches, defined as chunks of population activity separated by silences, in population (LFPs) or spike recordings; power-law distributions of avalanches are sometimes interpreted as revealing that the brain functions at a critical regime. I will present some thoughts and mathematical developments on simple models of large-scale stochastic networks, in order to uncover the complex interplay between stochastic and nonlinear dynamics in the emergence of these regimes. I will show that network structure, as well as increased noise levels, interact with nonlinear neurons activity to induce synchronization in large-scale systems, a phenomenon already reported in the biological literature on epilepsy. As for avalanche analysis, we will show that the data analysis methods used do not univocally reveal the presence of criticality: power-law scalings in LFPs avalanches may only be due to the noise in the LFP recordings, and power-laws in spiking data to Boltzmann’s molecular chaos (or propagation of chaos), a universal phenomenon in statistical systems.