Cayan Group launched the project, then called Infinity Tower, in 2005, the year SOM won the design contract; Arabian Business names Ross Wimer as SOM's design partner. SOM's project page gives 2006 as the year the design was finished. In December 2006 Arabtec was awarded the main construction contract.
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On 7 February 2007 the wall holding back the Dubai Marina water was breached and the excavated site flooded. Dewatering and remedial works delayed the project by more than a year, and work resumed on 15 June 2008. A later construction-period feature in Arabian Business reported that the tower had reached its 46th floor, with each slab rotating about one degree around a fixed cylindrical core.
The tower was originally expected to open in 2010. It received its final name, Cayan Tower, shortly before opening and was inaugurated in June 2013, which Cayan Group gives as the delivery date. According to Dezeen, it was the third skyscraper SOM completed in Dubai.
In June 2014 CTBUH named Cayan Tower Best Tall Building in the Middle East & Africa regional category, which qualified it to compete for the worldwide title later that year. In announcing the award, SOM described it as the tallest twisting tower in the world.