Basically, a limit must be at a specific point and have a specific value in order to be defined. Nevertheless, there are two kinds of limits that break these rules. One kind is unbounded limits -- limits that approach ± infinity (you may know them as "vertical asymptotes"). The other kind is limits at infinity -- these limits describe the value a function is approaching as x goes to ± infinity (you may know them as "horizontal asymptotes").
Some limits don't approach a specific value, but instead become boundlessly large as they approach the limiting value. For example, the limit of 1/x as we approach x=0 from the right. Learn about this type of limits and how it relates to vertical asymptotes.
For some expressions, as we increase x infinitely, approach a finite value. For example, 1/x approaches 0 as x becomes infinitely large. Learn about these types of limits, and how they relate to horizontal asymptotes.