Administrators can perform these actions only on a wiki on which they have been given adminship.
The role and expectations of administrators, as well as the policies surrounding their behavior, vary widely among the different projects. While administrators have more technical abilities than ordinary users, this should not be confused with authority, which is earned separately and given by the community. Some wiki sites may not even have adopted written policies for administrators or candidates for adminship. This is usually due to limited number of users and activities.
Some projects use different terms for administrators. For example, the English Wikiversity uses "custodian", while the Spanish Wikipedia uses what translates into "librarian".
All "administrative" actions are logged and reversible by any other administrator. The same principle applies to all the special permissions on MediaWiki, although some are not publicly logged: see for instance checkusers, who need to be at least a couple on each Wikimedia project to check each other. This makes their activity closely scrutinized by the community at large. In particular, it is comparable to the ius intercessionis or the Roman consuls' veto: an intrinsic system for consensual action, reciprocal control, and prevention of abuse. Its degeneration, when the system fails to actually prevent abuse and such powers have to be in fact exercised (multiple times) to reverse a previous action, is the so-called wheel war.
Administrators are subject to the global admin activity review policy, which stipulates that their rights may be removed if inactive for more than two years.