Systems-level neurophysiological data reveal coherent activity that is distributed across large regions of cortex. This activity is often thought of as an emergent property of recurrently connected networks. The fact that this activity is coherent means that populations of neurons may be thought of as the carriers of information, not individual neurons. Therefore, systems-level descriptions of functional activity in the network often find their simplest form as combinations of the underlying neuronal variables. In this paper, we provide a general framework for constructing low-dimensional dynamical systems that capture the essential systems-level information contained in large-scale networks of neurons. We demonstrate that these dimensionally-reduced models are capable of predicting the response to previously un-encountered input and that the coupling between systems-level variables can be used to reconstruct cellular-level functional connectivities. Furthermore, we show that these models may be constructed even in the absence of complete information about the underlying network.