Eldritch Obelisks are small structures that randomly generate in all overworld biomes, aside from ocean biomes and their variants. They are comprised of several outer pedestals and a single central pedestal, above which floats the obelisk itself. These pedestals sit on an obsidian and Eldrich Stone base, which stretches several blocks deep. While all Eldrich Obelisks share the same basic layout, they can be categorized into three types according to their mob spawns.
Mobless Obelisks - by far the most common. These are mostly aesthetic, although they are a good source of Eldrich Stone and like all obelisks, can be used in the Opening the Eye ritual.
Crimson Cult Obelisks - these are infrequent, but not terribly difficult to find. They spawn at world generation with four Crimson Clerics performing magic at the obelisk. These clerics will not attack unless players get quite close, or unless provoked. Instead they periodically summon Crimson Knights, which periodically despawn, so that at any time there are 2-6 knights milling about the obelisk (who will also not attack unless provoked or approached very closely). The clerics will not naturally despawn, but if killed will not respawn either. Would-be cultist farmers are therefore advised to only target the knights.
Guardian Obelisks - these are rare, but worth searching for. They repeatedly spawn 1-2 Eldritch Guardians. While weaker than their Outer Lands counterparts, these can still be very dangerous early on, but provide a reliable source of both Auram and Alienis, which are otherwise hard to come by.