The Warriors of God that make up the Host of Heaven, created after the Leviathans. They require the consent of whomever they wish to use as their vessel - typically a person of a specific bloodline. They work in an incredibly ranked hierarchy with archangels on top and regular angels filling up the ranks underneath. All angels speak Enochian as well as every other language on the planet. As of now, because the Apocalypse has been averted and both Lucifer and Michael are out of the Cage, angels are free to come and go from Heaven to earth and interact with humans without punishment.
Angels have Grace, essentially the essence that makes them angels, and it can be weakened just as any other source of strength, but it will always recover fully unless removed from the angel. The rank of an angel is very telling of their abilities (an archangel trumps all, Castiel’s brand of warrior angel is stronger than a Cherub, etc) but ranking within the garrisons needs to be remembered as well (Anna being stronger than Castiel, Uriel being a ‘specialist’). While in their vessels, the human’s body changes substantially the longer the angel is inside, as noted by Castiel saying that his blood is not human in season 6. Angels have a true form outside of their human vessels but only certain humans can perceive them without having their eyes burned out just the same as an angel’s true voice (we don’t know of any yet) but a human fallen angel can still listen to the conversations of angels.
Teleportation (what Dean terms ‘beaming’ but they can also fly with their wings, which can be hidden if they wish)
Healing (their vessels as well as humans)
Exorcism by touch (Rank of demons is also important here i.e Alistair being immune to the touch; also works on monsters, see Vampires in Mommy Dearest)
Supernatural perception (detecting beings humans can’t see)
Soul reading & channeling
Time travel (It should be noted that this takes an incredible amount of energy and considerably weakens the angel, especially when it is done without the consent of heaven.)
Gift of Revelation to prophets
Resurrection (Some, not all)
Matchmaking (specific to Cherubs/Cupids)
Destructive White Light (A Spirit Bomb with their Grace essentially)
Archangels can manipulate weather and have essentially perfected all the above abilities by virtue of being the oldest and the strongest of the angels. Gabriel is seen altering reality during his portrayal as a Trickster, but it is assumed the other three can also do this.
Exorcism (Only used by Alistair once and presumed to be known only to the oldest, most powerful of demons.)
Salt Crystal belonging to Lot's Wife
The Colt (not on the Archangels)
Archangels can kill other angels with a snap of their fingers (Anna’s death via Michael).
Eve is seen inhibiting Castiel’s powers and, as having been created before them, is perceived here to be at least as strong as an Archangel against them, though inhibiting all of an Archangel’s abilities is not within her range just as they cannot kill her with a simple snap.
The Cambion, Jesse Turner, is a valuable asset against angels. Castiel stated that he could destroy The Host with a single thought and even turned him into a toy.
It should be noted that an angel's abilities are not without limits - no one angel would be able to do all of these things, especially not at once. (ie, having a powerful character is not an excuse to god mod others)