Fixation constraints in visual tasks are ubiquitous in visual and cognitive neuroscience. Despite its widespread use, fixation requires trained subjects, is limited by the accuracy of fixational eye movements, and ignores the role of eye movements in shaping visual input. To overcome these limitations, we developed a suite of hardware and software tools to study vision during natural behavior in untrained subjects. We measured visual receptive fields and tuning properties from multiple cortical areas of marmoset monkeys who freely viewed full-field noise stimuli. The resulting receptive fields and tuning curves from primary visual cortex (V1) and area MT match reported selectivity from the literature which was measured using conventional approaches. We then combined free viewing with high-resolution eye tracking to make the first detailed 2D spatiotemporal measurements of foveal receptive fields in V1. These findings demonstrate the power of free viewing to characterize neural responses in untrained animals while simultaneously studying the dynamics of natural behavior.