Recent studies of visual statistical learning (VSL) have demonstrated that statistical regularities in sequences of visual stimuli can be automatically extracted, even without intent or awareness. Despite much work on this topic, however, several fundamental questions remain about the nature of VSL. In particular, previous experiments have not explored the underlying units over which VSL operates. In a sequence of colored shapes, for example, does VSL operate over each feature dimension independently, or over multidimensional objects in which color and shape are bound together? The studies reported here demonstrate that VSL can be both object-based and feature-based, in systematic ways based on how different feature dimensions covary. For example, when each shape covaried perfectly with a particular color, VSL was object-based: Observers expressed robust VSL for colored-shape sub-sequences at test but failed when the test items consisted of monochromatic shapes or color patches. When shape and color pairs were partially decoupled during learning, however, VSL operated over features: Observers expressed robust VSL when the feature dimensions were tested separately. These results suggest that VSL is object-based, but that sensitivity to feature correlations in multidimensional sequences (possibly another form of VSL) may in turn help define what counts as an object.