How does the visual system represent continuity in the constantly changing visual input? A recent proposal is that vision is serially dependent: Stimuli seen a moment ago influence what we perceive in the present. In line with this, recent frameworks suggest that the visual system anticipates whether an object seen at one moment is the same as the one seen a moment ago, binding visual representations across consecutive perceptual episodes. A growing body of work supports this view, revealing signatures of serial dependence in many diverse visual tasks. Yet, the variety of disparate findings and interpretations calls for a more general picture. Here, we survey the main paradigms and results over the past decade. We also focus on the challenge of finding a relationship between serial dependence and the concept of "object identity," taking centuries-long history of research into account. Among the seemingly contrasting findings on serial dependence, we highlight common patterns that may elucidate the nature of this phenomenon and attempt to identify questions that are unanswered.