A runner can miss a base, leave too soon on a caught fly ball, or pass another runner without being called out immediately. In many of those situations, the umpire waits for the defence to make a proper appeal before ruling on the mistake.
The most common appeal is a missed base. A runner must touch first, second, third, and home in order when advancing, and must retouch bases in reverse order when returning. The defence can also appeal that a runner left a base too early after a caught fly ball.
Other appeal situations exist, such as batting out of order, but missed-base and tag-up appeals are the base-running calls fans see most often.
The defence generally has to identify the runner's mistake by tagging the runner or the base involved while making the appeal obvious to the umpire. Exact mechanics can vary by rules code, especially at youth and school levels, but the principle is the same: the umpire does not guess the defence's intent.
For a missed base, the appeal is normally made at the base the runner missed. For leaving early on a caught fly ball, it is made at the base the runner had to retouch.
A runner who misses a base can often correct the mistake by returning and touching it before reaching a point where the rules no longer allow correction. The runner has to correct bases in the proper order, and cannot simply skip back through the defence after the play has moved beyond the legal correction window.
One important limit is that a runner generally may not return to fix a missed base after a following runner has scored. Leaving the field of play can also end the runner's ability to correct the miss.
An appeal out can change whether a run counts. If the appealed runner is forced, or if the batter-runner is appealed out before reaching first, runs on that play do not score when that out is the third out. If the appeal is a time play, the umpire judges whether the run scored before the appealed out.
In rare cases, the defence may make an advantageous appeal after an apparent third out. This is often called a fourth-out appeal because the defence is asking to replace the less useful third out with an appeal out that prevents a run.
On appeal plays, seeing the missed base is not always enough. The umpire may know the runner missed it, but the defence still has to appeal correctly. Baseball treats the missed base as a violation the defence must claim, not as an automatic call in every situation.
Touching the next base does not erase a missed base. The runner is treated as having advanced for the moment, but the defence can still appeal the missed base if the runner has not legally corrected it and the appeal deadline has not passed.