This state-of-the-art review provides an overview of the evolution of self-centering structures from early historical structures that inherently exhibited a recentering response to modern systems engineered for enhanced seismic resilience. From the early research investigations that were conducted since the 1960s, to the sharp increase of interest in this topic over the last two decades, self-centering seismic-resistant structures that can mitigate both damage and residual drifts following major earthquakes have seen significant advances. These systems achieve the intended self-centering response by either allowing for the rocking of primary structural elements in a controlled manner, commonly coupled with mechanical restraints and energy dissipation devices, or by including self-centering devices as main structural or supplemental structural members. To better explain the concepts and the underlying mechanics governing their seismic response, detailed schematic illustrations were developed in this article, highlighting the fundamentals behind each of these systems. This article covers a historical overview, presents the state of the research and of the art, discusses general design challenges and practical considerations, and concludes with future research needs to advance the development and broader application of self-centering systems in real structures.