Understanding the role of multiple cortical and subcortical circuits in cognitive processes is a current challenge for Systems Neuroscience. To address this, I design and implement computational models that connect large-scale neural circuitry to electrophysiology and behavior. In the first part of my talk, I will present a circuit model to understand the shared and unique roles of frontal and parietal cortices in a variety of cognitive tasks. I found that structural differences between these cortical areas map onto complementary dynamical regimes that subserve working memory and decision-making computations. Next, I consider the primate pulvinar, which is the largest part of the visual thalamus and is reciprocally connected to multiple visual and association cortical areas. I put forward a framework of pulvino-cortical interactions to clarify the pulvinar’s involvement in attention, confidence, and communication. Finally, I introduce a computational framework to analyze subcortical-cortical interactions during motor planning, constrained by multisite recordings in the mouse. I propose that subcortical inputs to the thalamus selectively gate cortical ‘dynamical modes’ relevant for movement. Overall, the modeling results support the existence of general computational principles underlying distributed and large-scale interactions in the brain.