Most oceanic islands are due to excess volcanism caused by thermal and/or compositional mantle melting anomalies. We call attention here to another class of oceanic islands, due not to volcanism but to vertical motions of blocks of oceanic lithosphere related to transform tectonics. Sunken tectonic islands capped by carbonate platforms have been previously identified along the Vema and Romanche transforms in the equatorial Atlantic. We reprocessed seismic reflection lines, did new facies analyses and 87Sr/86Sr dating of carbonate samples from the carbonate platforms. A 50 km long narrow paleoisland flanking the Vema transform, underwent subsidence, erosion, and truncation at sea level; it was then capped by a 500 m thick carbonate platform dated by 87Sr/86Sr at ∼11–10 Ma. Three former islands on the crest of the Romanche transverse ridge are now at ∼900 m bsl; they show horizontal truncated surfaces of oceanic crust capped by ∼300 m thick carbonate platforms, with 10–6 Ma Sr isotopic ages. These sunken islands formed due to vertical tectonics related to transtension/transpression along long-offset slow-slip transforms. Another tectonic sunken island is Atlantis Bank, an uplifted gabbroic block along the Atlantis II transform (SW Indian Ridge) ∼700 m bsl. A modern tectonic island is St. Peter and St. Paul Rocks, a rising slab of upper mantle located at the St. Paul transform (equatorial Atlantic). “Cold” tectonic islands contrast with “hot” volcanic islands related to mantle thermal and/or compositional anomalies along accretionary boundaries and within oceanic plates, or to supra-subduction mantle melting that gives rise to islands arcs.