....like an eagle....

... to the sea.

For my own reference - but I like to share:

The unmodified Fly spell can provide up to 12,000 ft of movement, or over 2 miles, if the caster Dashes every round. 

That's over 13.5 mph, or almost 22 kmph.

While under the effects of Haste, that's 360ft/round, 60ft/sec, or roughly 41 mph (~66 kph).  Sadly, only lasts a minute, but no one's ever getting away from a flying hasted PC!

Fly is concentration correct?

Quote from dmdave7178 >>

Fly is concentration correct?

 That is Correct

Any spell with a C next to the duration is concentration.

What are the carry weight restrictions on the fly spell? Can I carry a creature of the same size or smaller? What about someone small like a halfling?

Since the spells adds a movement speed to a character I would assume the normal encumbrance rules would apply, if the DM is using those. 

What if the recipient of the spell moves away from the caster (at full speed, for a long time)?  Is there a range at which the spell fails?

Quote from Graeys >>

What if the recipient of the spell moves away from the caster (at full speed, for a long time)?  Is there a range at which the spell fails?

The range only matters for the purpose of casting the spell. Once it takes effect, the target can go as far away from the caster as they want and the effect stays on them until the end of the duration or the caster stops concentrating on the spell for whatever reason.

DiceFarmer >>

While under the effects of Haste, that's 360ft/round, 60ft/sec, or roughly 41 mph (~66 kph).  Sadly, only lasts a minute, but no one's ever getting away from a flying hasted PC!

 ___________________________________

Actually that's 180ft/round and 30ft/second as a dash action only lets you move an additional amount equal to your movement, so that's 60x3

Unless the flier is a rogue or certain type of barbarian in which case they'd be able to get 60x4 ft a round by using their bonus action for 240ft/round and 40ft/second

With all that they're going at 20.45mph or 27.27mph (32.9kmph/ 43.9kmph)

Ahh... but Haste also doubles your speed!  With Haste, your Fly speed becomes 120ft/round!  You could then use your action to dash, move you speed, and dash again.  If your PC has a class feature that lets you use the bonus action to dash, your Flying Hasted speed would be 480ft/round, or about 55mph!

Someone moving that fast would complete the 100 metre dash is about 4.1 seconds! :-D

Quote from DiceFarmer >>

Ahh... but Haste also doubles your speed!  With Haste, your Fly speed becomes 120ft/round!  You could then use your action to dash, move you speed, and dash again.  If your PC has a class feature that lets you use the bonus action to dash, your Flying Hasted speed would be 480ft/round, or about 55mph!

Someone moving that fast would complete the 100 metre dash is about 4.1 seconds! :-D

 oop, don't know how I glossed over that, It's not the first time either, hah

only wizards can learn this

And Sorcerers. And Warlocks. And Artificers. And high level Arcane Tricksters.

Remember to have feather fall prepared or items that can give similar effect... or be the first person in your world to come up with a gliding suit

Simic Hybrid: Fly diagonally up 60 ft + Manta Glide 120 ft on your way down = 180ft horizontal movement in one turn? Is that really how this works? :D

Casting word is:

Aerielus Dramaticus

And Lore Bards with Magic Secrets...unless I'm mistaken?

yep my lore bard picked it up and fireball and causes all kinds of havoc