The Ziggurats are ancient temples to the goddess Ioun. At the time of the current campaigns, they tend to be very well-hidden underground structures. Most are not still in use for Ioun worship, but have been corrupted for other purposes.
Below the Slayer's Take guild hall in Vasselheim lies a sealed chamber containing a ziggurat. The chamber is inhabited by the gynosphinx Osysa. Osysa has a close connection with Ioun in the form of a Heartglass, a divination device inside the ziggurat that allows Osysa to watch over members of the guild, investigate quarry for guild contracts, watch over her mate, and see other things besides. This ziggurat is the only one Vox Machina have encountered that still functions as an active temple of Ioun.
The Whitestone ziggurat lies deep underground beneath the City of Whitestone (but is currently only readily accessible from tunnels dug from the Whitestone Castle) and was largely abandoned until the coming of the Briarwoods. It is somewhat implied that the ziggurat, along with the magical residuum from the whitestone mines, was what attracted the Briarwoods in the first place. The Briarwoods used the Whitestone ziggurat as a site to prepare a secret ritual for Vecna.
The Briarwoods' ritual, though enacted too early, did leave behind a strange, hovering black orb that sucked in anything that touched it and disabled all magic within a certain radius. Because this dispelling effect provided a measure of protection against magical espionage, the ziggurat was subsequently used as a war council room by Vox Machina and their allies in Whitestone.
Scanlan Shorthalt and Lionel Gayheart discovered a ziggurat on the continent of Marquet, within the Smouldercrown Mountains. Here Delilah conducted a second, or possibly third, ritual for Vecna before Vox Machina could interfere.