Despite the complexity of biological neural networks, simplified theoretical descriptions can be a powerful tool to study their dynamics and have led to profound insights. However, many of these results have been obtained for biologically unrealistic limiting cases, because even for simple network models it becomes quickly too complicated to obtain analytical solutions. Here, we propose to study “rotator networks,” which are considerably simpler than real spiking networks and therefore more amenable to mathematical analysis. A typical problem is to understand the self-generated fluctuations of neural activity, which are due to the quenched disorder of random synaptic connections and can show a rich temporal correlation structure shaped by the network dynamics. They need to be determined self-consistently, as in recurrent networks typical inputs equal typical outputs. For rotator networks with Gaussian connectivity matrices, dynamic mean-field theory has allowed to obtain a semi-analytical expression for the power spectra of the network noise, but for networks composed of excitatory and inhibitory units with finite connection probability this solution ceases to be exact. While we have shown that using a cumulant expansion, dynamic mean-field theory can be extended to account for non-Gaussian fluctuations that are cause by correlated external inputs, finding the correct expression for the case of purely excitatory or inhibitory connections remains an open problem.