Modern computational models of attention predict fixations using saliency maps and target maps, which prioritize locations for fixation based on feature contrast and target goals, respectively. But whereas many such models are biologically plausible, none have looked to the oculomotor system for design constraints or parameter specification. Conversely, although most models of saccade programming are tightly coupled to underlying neurophysiology, none have been tested using real-world stimuli and tasks. We combined the strengths of these two approaches in MASC, a model of attention in the superior colliculus (SC) that captures known neurophysiological constraints on saccade programming. We show that MASC predicted the fixation locations of humans freely viewing naturalistic scenes and performing exemplar and categorical search tasks, a breadth achieved by no other existing model. Moreover, it did this as well or better than its more specialized state-of-the-art competitors. MASC's predictive success stems from its inclusion of high-level but core principles of SC organization: an over-representation of foveal information, size-invariant population codes, cascaded population averaging over distorted visual and motor maps, and competition between motor point images for saccade programming, all of which cause further modulation of priority (attention) after projection of saliency and target maps to the SC. Only by incorporating these organizing brain principles into our models can we fully understand the transformation of complex visual information into the saccade programs underlying movements of overt attention. With MASC, a theoretical footing now exists to generate and test computationally explicit predictions of behavioral and neural responses in visually complex real-world contexts. SIGNIFICANCE STATEMENT The superior colliculus (SC) performs a visual-to-motor transformation vital to overt attention, but existing SC models cannot predict saccades to visually complex real-world stimuli. We introduce a brain-inspired SC model that outperforms state-of-the-art image-based competitors in predicting the sequences of fixations made by humans performing a range of everyday tasks (scene viewing and exemplar and categorical search), making clear the value of looking to the brain for model design. This work is significant in that it will drive new research by making computationally explicit predictions of SC neural population activity in response to naturalistic stimuli and tasks. It will also serve as a blueprint for the construction of other brain-inspired models, helping to usher in the next generation of truly intelligent autonomous systems.