The phrasing for critical hits in 5e is the general attack. This counts for anything with an attack roll, a monster attack, an adventurer attack, a generic NPC attack and a wizard (of any stripe's) spell attack roll. Here's where it talks about a natural 20:
If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target’s AC. In addition, the attack is a critical hit, as explained later in this chapter. (Basic D&D p73)
Though "doubling" is a bit misleading. Here's the critical hit mechanic:
When you score a critical hit, you get to roll extra dice for the attack’s damage against the target. Roll all of the attack’s damage dice twice and add them together. Then
add any relevant modifiers as normal. To speed up play, you can roll all the damage dice at once. (Basic D&D p75)
The dice rolled are doubled (static mods are only counted once). Believe it or not this is only slightly more damaging on average than 4e's crit mechanic (though it is swingier). Let's look at a d8 in each mechanic. In 4e a d8 for damage would result in 8 damage on a crit. In 5e it would result in 2d8 rolled for an average of 9 (min of 2, max of 16). Obviously a good roll makes this a way swingier result, however, an average roll only makes this one point of damage better. This doesn't factor in the fact that in 4e you regularly add in your weapon's crit dice to your attacks, and this would lead to an average slightly above or about the same as 5e's crit damage.
Note: if you watch the D&D live streams they were talking about a fight against an Ogre with Fighter levels who kept critting them and dropping their PCs. (I think that's the right stream, it might have been the other Q&A).