Understanding how large populations of neurons communicate in the brain at rest, in response to stimuli, or to produce behavior as well as how brain function relates to structure are fundamental open questions in neuroscience. Many approach this by estimating the intrinsic functional neuronal connectivity using probabilistic graphical models. But there remain major statistical and computational hurdles to estimating graphical models from new large-scale calcium imaging technologies and from huge projects which image up to one hundred thousand neurons across multiple sessions in the active mouse brain. In this talk, I will highlight a number of new graph learning strategies my group has developed to address many critical unsolved challenges arising with large-scale neuroscience data. Specifically, we will focus on Graph Quilting, in which we derive a method and theoretical guarantees for graph learning from non-simultaneously recorded neurons. We will also highlight theory and methods for graph learning with latent variables induced by unrecorded neurons via thresholding, graph learning for spikey neuronal activity data via Subbotin graphical models, and computational approaches for graph learning from enormous numbers of neurons via minipatch learning. Finally, we will demonstrate the utility of all approaches on synthetic data as well as real calcium imaging data for the task of estimating functional neuronal connectivity.