The Globe of Invulnerability spell states:
Any spell of 5th level or lower cast from outside the barrier can't affect creatures or objects within it, even if the spell is cast using a higher level spell slot. Such a spell can target creatures and objects within the barrier, but the spell has no effect on them. Similarly, the area within the barrier is excluded from the areas affected by such spells.
The Misty Step spell states:
you teleport up to 30 feet to an unoccupied space that you can see.
The Dimension Door spell states:
You teleport yourself from your current location to any other spot within range. You arrive at exactly the spot desired.
Let's say that Bob casts Globe of Invulnerability; then Fred, who's outside Bob's globe, wants to teleport inside it (using Misty Step, or Dimension Door). Can Fred do that, or does the globe block outsiders from teleporting inside with a spell?
Best Answer
Both Misty Step and Dimension Door work unimpeded
Misty Step and Dimension Door, when cast on creature outside the barrier, do not affect or target creatures or objects within the barrier, and they don't affect an area. Furthermore, Globe of Invulnerability does not block vision (required for Misty Step), nor does it prevent targeting of points within it (required for Dimension Door). So it seems that nothing in the text of Globe of Invulnerability would interfere with either of these spells.
Other teleportation spells might be affected
Note that while the two specific spells in the question are not blocked, not every teleportation spell is guaranteed to get through. For example, suppose you cast Steel Wind Strike targeting only creatures within the globe. The relevant parts of the spell's text are:
If all targets are unaffected due to the protection of the globe, then you have not hit or missed any of them, because you have not attacked them. Therefore, you cannot teleport using the spell, since you have no valid targets to teleport next to.
So, it's important to read the text of the specific spell you want to use to determine what interaction it will have with Globe of Invulnerability.