The strings we have discussed so far have been "closed strings": they close back on themselves in a loop, so they don't have any edges. However, string theory can also contain "open strings" which look like line segments instead of loops. The main new feature of open strings is their endpoints, which (not surprisingly) behave in many ways like point particles.
As illustrated here, open strings can interact by joining their endpoints together or by splitting apart. But even though the string's "worldsheet" now has boundaries, there still aren't any unique "special points" where interacting strings join up: just as before, string interactions are smooth.
Although it is not illustrated here, the interior of an open string can also interact like a closed string, by "pinching off" a new closed loop (or by absorbing one). An open string can even turn entirely into a closed string if its two endpoints came together and merged. And similarly, when open strings are allowed a closed string can split in the middle and become an open string. So every version of string theory that allows open strings must also include closed strings (but there are versions of the theory in which closed strings aren't allowed to split into open ones).
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