I encountered a situation where I was Frightened of a large creature. By the words of the Frightened condition:

The creature can’t willingly move closer to the source of its fear.

Could you use the Misty Step spell (or some other means of teleportation) to get closer, since the rules only specifically mention moving closer?

The closest thing I could find was this question about Booming Blade, which seems to suggest that this should be allowed.

Yes, technically.

By RAW, teleportation does not count as movement.

What counts as movement is implied in the Basic Rules in the section on Adventuring: Movement. Though not necessarily an exclusive enumeration of all possible forms of movement, this section details the following as forms of movement: walking, climbing, jumping, swimming, crawling, and marching. None of these fits the description of instantaneously appearing at another location, so by implication teleportation doesn't count as a form of movement.

In addition, no teleportation spell or feature mentions using one's speed or being limited by one's speed, whereas the Combat: Movement and Position rules explain that movement on your turn involves moving a distance up to your speed by walking, jumping, climbing, or swimming, deducting the distances cumulatively from your speed. Teleportation doesn't fit this description either.

Although there's no rule that explicitly states "teleportation isn't movement," the passages above make it clear that the RAW doesn't include teleportation as a kind of movement.

But it's almost certainly not intended.

By RAI, the point of the frightened condition is clear: if you're frightened, you're too afraid to willingly approach, close the distance with, or otherwise cause yourself to become closer to the source of your fear. The rules are written in simple language ("move closer to"), not technically less ambiguous but unnatural language ("cause yourself via your speed, teleportation, or any other means to become closer to"). That sort of language wouldn't aid comprehension. The rules are supposed to be read at face value, not as a legal document.

So it's pedantic to suggest that teleportation doesn't count, despite the RAW, and a DM could reasonably forbid getting closer to a source of fear via teleportation. I rule in this fashion at my table because the frightened creature in the narrative isn't the rules lawyer at the table; the player might be calm and collected enough to be picky, but the creature just wants to get away.

In the interests of a smooth and non-antagonistic experience at the table, it's probably best if everyone is on the same page with the DM before attempting anything clever. If you're the player, you'd probably better ask how the DM would rule before expecting that teleportation would work.

If you are subject to being Frightened then you should be role playing being frightened, not trying to rules-lawyer an argument that teleportation is not specifically listed in the PHB section on movement. Frightened does not place a physical restriction on movement that can be circumvented through magical means. It creates an abject and irrational fear, a phobia, that makes you absolutely, completely and in all other ways unwilling to get closer. Period.

If that thing you are afraid of was not a large creature, but was instead a swirling vortex that is going to suck your character inside, chop you into little pieces, then throw the still living bits into the burning pit of Hell, would teleporting closer be any less scary than walking closer? Because that is how your character perceives the thing that it is making them Frightened. If another player or creature tries to drag you closer to the subject of your fear then you should be resisting them more fiercely than a feral cat being dragged towards bathwater. If you are in a raft drifting on a river and the current is carrying you towards the subject of your fear then you should either be trying to row against the current or jumping off the raft to swim for the opposite shore. Even if you are wearing armor and don't know how to swim. You are not thinking sanely, you are only thinking about staying away from that thing.

I believe that NautArch's answer to What is "closer" for the purposes of the frightened condition? could also be copy/pasted as an answer to this question and be equally valid as it is there.

It's certainly a violation of the spirit of the rule but I would not categorically prohibit it. Rather, I would look at the threat the creature poses. You're frightened of a creature without ranged attacks and which is confined to the ground--I would permit teleporting to an inaccessible platform even if that was closer to the creature--but only so long as there wasn't a point of equivalent safety that was also farther away.

No, teleporting to the target means you are now closer than you were

"Moving" closer means being physically closer

I think you may be reading more into this than necessary, but the language of can't move closer is really as simple as can not get physically closer. If at any point in the target's turn they try to be physically closer to the source of their fear, they can not continue and must choose a new path.

As soon as your actions put you in a position that is closer than where you were when first affected, you must not choose to be closer.

Scary monsters!

Remember, you are frightened! You do not want to get anywhere physically closer to your fear. It's all about proximity, that's all your thinking about. It's not about time to travel to get to them, it's about being close to them. And that's exactly where you don't want to be. You are not thinking logically, you are reacting irrationally to your fear.

Fear is a funny thing

The role-playing goal here is to play scared. If you've got an idea that plays that, and aren't trying to get close enough for a spell or attack, then by all means describe it to the DM. Rule of Cool is cool.

No. They can not teleport closer to them.

Under Movement and Position in the PHB, it states the following:

Your movement can include jumping.....

emphasis mine

It makes no suggestion that this covers all forms of movement, nor could it. According to this "teleport is not movement" interpretation, swinging on a vine, driving a wagon, falling, riding in an out of control mine cart, or allowing a buddy to push you would not be movement. I think we can agree that each example I used, E pur si muove.

Just because it is not listed under examples of movement does not mean it is not movement.