Praise be to Allah.

Belief in angels is one of the six pillars of belief
Belief in angels is one of the six pillars of faith without which there is no faith. Whoever does not believe in any of these pillars is not a believer (mumin). These pillars are belief in: Allah, His angels, His Books, His Messengers, the Last Day, and that predestination, both good and bad, comes from Allah.

Who are the Angels?
Angels are a part of the world of the “Unseen” which we cannot comprehend. Allah has told us about them in many places in the Quran and via His Prophet Muhammad (peace and blessings of Allah be upon him). There follows a number of proven reports concerning the angels, which hopefully will make you realize the greatness of the Creator and the greatness of this religion which has told us so much about them:

Of what are the Angels created?
They are created from light, as ‘Aishah (may Allah be pleased with her) reported: "The Messenger of Allah (peace and blessings of Allah be upon him) said: ‘The angels are created from light, just as the jinn are created from smokeless fire and mankind is created from what you have been told about.’" [Muslim].

When were the Angels created?
​​​​​We have no knowledge of precisely when they were created, because there is no text to tell us this. But they were created before mankind for certain, because the Quran says (interpretation of the meaning): "Behold, your Lord said to the angels: ‘I will create a vicegerent on earth.’" [2:30] The fact that Allah told them of His intention to create man indicates that they already existed.

The great size of Angels
Allah says concerning the angels of Hell:
"O you who believe! Save yourselves and your families from a Fire whose fuel is men and stones, over which are (appointed) angels stern and severe, who flinch not (from executing) the commands they receive from Allah, but do (precisely) what they are commanded." [66:6]
The greatest of all the angels is Jibreel, upon whom be peace, who was described in the following report:
"From ‘Abdullah ibn Mas‘ood (may Allah be pleased with him) who said: the Messenger of Allah (peace and blessings of Allah be upon him) saw Jibreel in his true form. He had six hundred wings, each of which covered the horizon. There fell from his wings jewels, pearls and rubies, only Allah knows about them." It was reported by Ahmad in al-Musnad, and Ibn Katheer said in al-Bidayah that its isnad (chain of narrators) is jayyid (good).

The Messenger of Allah (peace and blessings of Allah be upon him) said, describing Jibreel:
"I saw Jibreel descending from heaven, and his great size filled the space between heaven and earth." [Muslim].
Among the greatest angels are those who carry the Throne (of Allah), who were described in the following report:
"From Jabir ibn ‘Abdullah (may Allah be pleased with him) from the Prophet (peace and blessings of Allah be upon him), who said: ‘I have been given permission to speak about one of the angels of Allah who carry the Throne. The distance between his ear-lobes and his shoulders is equivalent to a seven-hundred-year journey.’" [Abu Dawood].

Description of Angels
Angels have wings
Allah says (interpretation of the meaning):
"Praise be to Allah, Who created (out of nothing) the heavens and the earth, Who made the angels messengers with wings - two, or three, or four (pairs) adds to Creation as He pleases: for Allah has power over all things." [35:1]

Beauty of the Angels
Allah said, describing Jibreel, upon whom be peace (interpretation of the meaning):
"He [the Prophet] has been taught by one Mighty in Power, Dhoo Mirrah (free from any defect in body and mind), then he rose and became stable." [53:5-6]

Ibn ‘Abbas said: "‘Dhoo Mirrah means that he has a beautiful appearance." Qutadah said: "He is tall and beautiful."
The idea that angels are beautiful is firmly established in all people’s minds, so much so that they liken a beautiful human to an angel, as the women said about Yoosuf:
". . . When they [the women] saw him, they did extol him and (in their amazement) cut their hands: they said: ‘Allah preserve us! No mortal is this! This is none other than a noble angel!’" [12:31]

The differences in size and status of the Angels
The Angels are not all of one size or status; there are differences between them just as there are differences in virtue. The best of them are those that were present at the battle of Badr, as is stated in the hadeeth narrated by Mu‘adh ibn Rifa‘ah al-Zuraqi from his father, who had been one of the people present at Badr. He said: "Jibreel came to the Prophet (peace and blessings of Allah be upon Him) and asked, ‘How do you rate the people among you who were present at Badr?’ He said: ‘They are the best of the Muslims,’ or something similar. [Jibreel] said: ‘So it is with the angels who were present at Badr.’" [al-Bukhaari].

The Angels do not eat or drink
This is indicated by the conversation between Ibrahim, the "friend" of Allah, and the angels who visited him.
Allah says (interpretation of the meaning):
"Then he turned quickly to his household, brought out a fatted calf, and placed it before them. He said, ‘Will you not eat?’ (When they did not eat), he conceived a fear of them. They said: ‘Fear not,’ and they gave him glad tidings of a son endowed with knowledge." [51:26-28]
Elsewhere, Allah says (interpretation of the meaning):
"But when he [Ibrahim] saw their hands went not towards the (meal), he felt some mistrust of them, and conceived a fear of them. They said: ‘Fear not: we have been sent against the people of Lut.’" [11:70]

The Angels do not get bored or tired of remembering and worshipping Allah
Allah says (interpretation of the meaning):
"They celebrate His praises night and day, nor do they ever slacken." [21:20]

". . . For in the presence of your Lord are those who celebrate His praises by night and by day. And they never become tired (nor feel themselves above it)." [41:38]

Number of Angels
The angels are many, and their number is known only to Allah. The Prophet (peace and blessings of Allah be upon him) said, describing the Much-Frequented House (al-Bayt al-M’amoor) in the seventh heaven:
"Then I was taken up to the Much-Frequented House: every day seventy thousand angels visit it and leave, never returning to it again, another [group] coming after them." [al-Bukhaari].
‘Abdullah (may Allah be pleased with him) said: "The Messenger of Allah (peace and blessings of Allah be upon him) said: ‘Hell will be brought forth that day by means of seventy thousand ropes, each of which will be pulled by seventy thousand angels." [Muslim].

Names of Angels
The angels have names, but we know only the names of a few of them. We have to believe in the names reported in the Quran and Sunnah (prophetic teachings) texts, as a part of general belief in the angels. Among the names of angels that are known to us are:

(1) Jibreel and (2) Mikail
"Say: Whoever is an enemy to Jibreel - for he brings down the (revelation) to your heart by Allah’s will, a confirmation of what went before, and guidance and glad tidings to those who believe -
Whoever is an enemy to Allah, and His angels and prophets, to Jibreel and Mikail - Lo! Allah is an enemy to those who reject faith." [2:97-98

(3) Israfil
From Abu Salamah ibn ‘Abd al-Rahman ibn ‘Awf, who said: "I asked ‘Aishah, the Mother of the Believers, about what the Prophet (peace and blessings of Allah be upon him) used to start his prayer with when he got up to pray at night (qiyam al-layl). She said: ‘When he got up to pray at night, he would start his prayer (with the words): ‘O Allah, Lord of Jibreel, Mikail and Israfil, Creator of heaven and earth, Knower of the unseen and the seen, You are the Judge of the matters in which Your slaves differ; guide me with regard to disputed matters of truth by Your permission, for You guide whomever You will to the straight path.’" [Muslim].

(4) Malik
He is the Keeper of Hell, as Allah says (interpretation of the meaning): "They [the people in Hell] will cry: ‘O Malik! Would that your Lord put an end to us!’" [43:77]

(5) Munkar and (6) Nakeer
[b]From Abu Hurayrah (may Allah be pleased with him) who said: "The Messenger of Allah (peace and blessings of Allah be upon him) said: ‘When the deceased is buried (or he said: when one of you is buried), there come to him two blue-black angels, one of whom is called Munkar and the other Nakeer. They ask him, ‘What did you used to say about this man?’ and he says what he used to say: ‘He is the slave and Messenger of Allah: I bear witness that there is no god except Allah and that Muhammad is the slave and Messenger of Allah. They say, ‘We knew beforehand that you used to say this.’ Then his grave will be widened for him to a size of seventy cubits by seventy cubits and it will be illuminated for him. Then they tell him, ‘Sleep.’ He says, ‘Go back to my family and tell them.’ They tell him, ‘Sleep like a bridegroom whom no-one will wake up except his most beloved,’ until Allah raises him up. If (the deceased) was a hypocrite, he says, ‘I heard the people saying something so I said something similar; I do not know.’ They say: ‘We knew beforehand that you used to say this.’ The earth will be told to squeeze him, so he will be crushed until his ribs are interlocked, and he will remain like that until Allah raises him up.’" [al-Tirmidhi].[/b]

(7) Haroot and (.8.) Maroot
Allah says (interpretation of the meaning):
". . . and such things as came down at Babylon to the angels Haroot and Maroot . . ." [2:102]
". . . and none can know the forces of your Lord, except He. And this is nothing other than a warning to mankind." [74:31]

Source IslamQA

Also read Belief in Angels 2 here on Nairaland

Angel are Allah's creations without free will like humans.

This is worth remembering!