A wizard flies very high over the battlefield using his Fly spell. But he wants to quickly descend and join the fight.
Does he have to descend at 60'/round?
Yes, but ...
Or during the ten-minute duration, can he pause the spell, plummet huge distances quickly, and then level off? (And, if so, could he also attack the same turn?)
No, but ...
I imagine he certainly could end the spell, plummet, and then recast it mid-air, but that would eat up his action and an extra spell slot.
Yes, but ...
The rules for flying are:
Flying creatures enjoy many benefits of mobility, but they must also deal with the danger of falling. If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of the ability to move, the creature falls, unless it has the ability to hover or it is being held aloft by magic, such as by the fly spell.
So a creature that can't hover and is flying without "being held aloft by magic" will fall if they become prone or have their movement reduced to 0. It costs no movement to become prone and half its movement to stop being prone. This will allow them to fall. However, this is explicitly not available to the Fly spell. If you fall prone, or your speed drops to 0, you don't fall.
Notwithstanding, under the core rules, falling is likely to be a terminal option. When you fall, you fall all the way down instantly: whether that be 5 feet or 5 miles. There are optional rules in Xanathar's that give a falling speed of 500 feet each round - again, this is instantaneous: fall prone (or end the Fly spell which you can do because it is a Concentration spell), fall 500 feet, stand up (or cast Fly again) and stop falling. It takes some very specific circumstances (i.e. being almost exactly 500 feet above where you want to be and definitely more than 500 feet above the ground) to pull this off.
Within the parameters of the game’s action economy this makes perfect sense. One action, one bonus action, one reaction, move up to your speed, and one free object interaction is all you get. Anything that breaks that is potentially game breaking.
There are ways for creatures to appear out of nowhere as it were - teleportation for example - but these almost always have a cost.
If you’re concerned that this is not a good simulation a) you are playing the wrong game; nothing in D&D is a good simulation, and b) no one would do this in the real world; the risk of a mid air collision is too great. Collisions in aerial dogfights and between skydivers are not uncommon and often fatal.
I refer to the same passage that has been quoted in the other answers (PHB p. 191):
If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of the ability to move, the creature falls, unless it has the ability to hover or it is being held aloft by magic, such as by the fly spell.
(Emphasis added). This means, while under the fly spell you will not be able to fall, also not when "dropping prone".
If you cast the fly spell upon yourself (or the caster cooperates), you or they could end concentration on the spell, causing the spell to end. At that point, unless you have a natural fly speed, you will be falling.
On p. 183 PHB:
A fall from a great height is one of the most common hazards facing an adventurer. At the end of a fall, a creature takes 1d6 bludgeoning damage for every 10 feet it fell, to a maximum of 20d6. The creature lands prone, unless it avoids taking damage from the fall.
There are no specifics about the fall in the core rules. Your DM either can rule it is immediate, or based on the assumption that everyday things behave as we would expect them to, they could also rule that there is a maxium drop rate due to air resistance and such per round. Variant rules in XGE (p.77) offer 500 feet per round:
When you fall from a great height, you instantly descend up to 500 feet. If you're still falling on your next turn, you descend up to 500 feet at the end of that turn. This process continues until the fall ends, either because you hit the ground or the fall is otherwise halted
If you are using such a rule, you could try and take other actions to regain the ability to fly before hitting the ground. Depending on the height you may have leisure to do so.
If the height is less than what you would drop in one round: ending concentration is not an action, so you likely could take a triggered action for the round where you fall to re-cast Fly shortly before hitting the ground&. This of course would cost you another spell slot use.
If you are interested, this answer provides an excellent summary of the mechanics and timing of falling.
& Thanks to Thomas Markov for finding this.
