Many functional neuroimaging modalities (e.g., fMRI, EEG, dynamic PET) produce, for each subject, a collection of time courses observed across brain regions, sensors, or sources. This talk outlines a body of work that uses a multivariate functional data framework for representing the resulting spatial and temporal dependence, with conditional spatial dependence being of primary interest.  Several formulations and approaches to functional graphical models, in which nodes correspond to entire component processes at each spatial location and edges encode conditional relationships between them, will be described, including both Gaussian and non-Gaussian formulations.  A central challenge is that functional covariance operators are compact and generally lack bounded inverses. We will then examine how notions covariance separability across space and time can provide parsimonious representations, facilitate graphical modeling, and be assessed empirically. Finally, in connection with the Gaussian case, we will discuss recent approaches to sparse functional precision operator estimation.