Understanding how neurons in the primary visual cortex (V1) of primates respond to visual patterns has been a major focus of research in neuroscience for many decades. Numerous different experimental techniques have been used to provide data about how the spatiotemporal patterns of light projected from the visual environment onto the retina relate to the spatiotemporal patterns of neural activity evoked in the visual cortex, across disparate spatial and temporal scales. However, despite the variety of data sources available (or perhaps because of it), there is still no unified explanation for how the circuitry in the eye, the subcortical visual pathways, and the visual cortex responds to these patterns. This thesis outlines a research project to build computational models of V1 that incorporate observations and constraints from an unprecedented range of experimental data sources, reconciling each data source with the others into a consistent proposal for the underlying circuitry and computational mechanisms. The final mechanistic model is the first one shown to be compatible with measurements of: (1) temporal firing-rate patterns in single neurons over tens of milliseconds obtained using single-unit electrophysiology, (2) spatiotemporal patterns in membrane voltages in cortical tissues spanning several square millimeters over similar time scales, obtained using voltage-sensitive-dye imaging, and (3) spatial patterns in neural activity over several square millimeters of cortex, measured over the course of weeks of early development using optical imaging of intrinsic signals. Reconciling this data was not trivial, in part because single-unit studies suggested short, transient neural responses, while population measurements suggested gradual, sustained responses. The fundamental principles of the resulting models are (a) that the spatial and temporal patterns of neural responses are determined not only by the particular properties of a visual stimulus and the internal response properties of individual neurons, but by the collective dynamics of an entire network of interconnected neurons, (b) that these dynamics account both for the fast time course of neural responses to individual stimuli, and the gradual emergence of structure in this network via activity-dependent Hebbian modifications of synaptic connections over days, and (c) the differences between single-unit and population measurements are primarily due to extensive and wide-ranging forms of diversity in neural responses, which become crucial when trying to estimate population responses out of a series of individual measurements. The final model is the first to include all the types of diversity necessary to show how realistic single-unit responses can add up to the very different population-level evoked responses measured using voltage-sensitive-dye imaging over large cortical areas. Additional contributions from this thesis include (1) a comprehensive solution for doing exploratory yet reproducible computational research, implemented as a set of open-source tools, (2) a general-purpose metric for evaluating the biological realism of model orientation maps, and (3) a demonstration that the previous developmental model that formed the basis of the models in this thesis is the only developmental model so far that produces realistic orientation maps. These analytical results, computational models, and research tools together provide a systematic approach for understanding neural responses to visual stimuli across time scales from milliseconds to weeks and spatial scales from microns to centimeters.