Anarchy is a political structure where there’s basically no one in charge, right? But wouldn’t that just create a power vacuum that would filled by organized crime, corporations, etc.? Then, after that power vacuum is filled, we’re right back at square one, and someone is in charge.
Are there any political theorists that have come up with a solution to this problem?


‘Basically no one in charge’ is not exactly correct. Heirarchies are allowed to exist, but ideally should be as brief and flat as possible.
My best understanding of the end-goal is an intermeshing alliance of small democratic collectives working together to provide for one another. This type of system has existed previously, such as with the various tribes across the Americas which often traded and collaborated with one another. In contrast with previous times, there is vastly more understanding of how the world works now, and thus many more possible projects to strive towards.
There is also no expectation of some supposed utopia from this, as i understand - conflicts are still expected to flair up every now and again. The main aim is for equality and the absence of a single constant power structure which oppresses and dictates the conditions of all, but instead that there is a democratic collaberation defining the conditions for folks involved.
Pretty much describes the US in 1781. The Founding Fathers were essentially trying to create a viable anarchy themselves but kept having to make compromises.
Sounds a lot like a bunch of small states to me.
States have governors, towns have mayors, and in anarchist theory none of those heirarchal positions would exist. Usually, heirarchies are formed in order to complete projects and those heirarchies are supposed to disappear once the project is complete. Can’t really have a state without a legislative body dictating it.
The original definition of state is different from the western nuspeak one that means government
the point being that there will be government, just horizontally managed.