Angels were involved in the giving of the law

Acts 7:53 you who have received the law that was given through angels but have not obeyed it.

Galatians 3:19 Why, then, was the law given at all? It was added because of transgressions until the Seed to whom the promise referred had come. The law was given through angels and entrusted to a mediator.

Hebrews 2:2 For since the message spoken through angels was binding, and every violation and disobedience received its just punishment, ...

Deuteronomy 33:2 He said: "The LORD came from Sinai and dawned over them from Seir; he shone forth from Mount Paran. He came with myriads of holy ones from the south, from his mountain slopes.
Psalm 68:17 The chariots of God are tens of thousands and thousands of thousands; the Lord has come from Sinai into his sanctuary.

Matthew Henry comments on Acts 7:53 that the law is said to be received by the disposition of angels, because angels were employed in the solemnity of giving the law, in the thunderings and lightnings, and the sound of the trumpet. It is said to be ordained by angels (Gal. 3:19 ), God is said to come with ten thousand of his saints to give the law (Deu. 33:2 ), and it was a word spoken by angels, Heb. 2:2 . This put an honour both upon the law and the Lawgiver, and should increase our veneration for both. But those that thus received the law yet kept it not, but by making the golden calf broke it immediately in a capital instance.

Barnes notes that the phrase given through angels has been supposed to mean that the Law was given “amidst” the various ranks of angels, being present to witness its promulgation. Others suppose that the angels were employed as agents or instruments to communicate the Law. All that the expression fairly implies is that the Law was given amidst the attending ranks of angels, as if they were summoned to witness the pomp and ceremony of giving “law” to an entire people, and through them to an entire world. It should be added, moreover, that the Jews applied the word “angels” to any messengers of God; to fire, and tempest, and wind, etc. And all that Stephen means here may be to express the common Jewish opinion that God was attended on this occasion by the heavenly hosts, and by the symbols of his presence, fire, and smoke, and tempest.

Angels can destroy people

1 Chronicles 21:15 And God sent an angel to destroy Jerusalem. But as the angel was doing so, the LORD saw it and relented concerning the disaster and said to the angel who was destroying the people, "Enough! Withdraw your hand." The angel of the LORD was then standing at the threshing floor of Araunah the Jebusite

1 Corinthians 10:10 And do not grumble, as some of them did - and were killed by the destroying angel.

Exodus 12:23c and he will not permit the destroyer to enter your houses and strike you down.

Acts 12:23 Immediately, because Herod did not give praise to God, an angel of the Lord struck him down, and he was eaten by worms and died. 

More than once we hear of angels involved in the act of destroying people, killing them. It is not entirely clear whether such angels may be fallen or unfallen. This appears to be what happened in David's time, although given the reference to the angel of the LORD, it may be God himself who is in mind. Paul suggests in the New Testament that a destroying angel was responsible for putting people to death in the wilderness. The destroyer of Exodus 12 is popularly thought of as the angel of death and this may be the reference here too. In Acts Herod is killed by an angel who inflicts a terrible disease on him.

Angels are always in God's immediate presence

Luke 12 8, 9 I tell you, whoever publicly acknowledges me before others, the Son of Man will also acknowledge before the angels of God. But whoever disowns me before others will be disowned before the angels of God.

Here the repeated phrase before the angels of God is another way of speaking of the immediate presence of God (see the parallel in Matthew 10:32, 33). We learn, therefore, with regard to angels, that they are always in God's immediate presence. What we also learn, however, is that believers ought to always be aware of an invisible world, the world of angels that is the world that really counts. So often we are aware of what men see and what they think but more important is what the angels see and what they think. When tempted to deny the Lord, think of the angels.
Revelation 3:5 is parallel in part
The one who is victorious will ... be dressed in white. I will never blot out the name of that person from the book of life, but will acknowledge that name before my Father and his angels.Also relevant is Luke 15:10, which we tend to think of as referring to angels but is really referring to God himself
In the same way, I tell you, there is rejoicing in the presence of the angels of God over one sinner who repents.
In Luke 1:19 Gabriel reveals that he stands always in the presence of God.

Angels are just, good, wise and discerning

2 Samuel 14:17, 20 “And now your servant says, ‘May the word of my lord the king secure my inheritance, for my lord the king is like an angel of God in discerning good and evil. May the LORD your God be with you.’ ” ... "Your servant Joab did this to change the present situation. My lord has wisdom like that of an angel of God--he knows everything that happens in the land."

(Also see 19:27 And he has slandered your servant to my lord the king. My lord the king is like an angel of God; so do whatever you wish.) 

These words spoken by the wise woman of Tekoa in two instances are really asides and we should be careful not to make too much of them. They do appear, however, to recognise a wisdom and discernment in the minds of angels that is beyond what we ordinarily find among men. Justice and goodness are also implied. These creatures are highly intelligent and they have not only a mental dexterity but also a moral integrity that remains untouched by sin. This enables them to know good from evil with great insight.

Angels do not marry or have sexual relations

Matthew 22:30 At the resurrection people will neither marry nor be given in marriage; they will be like the angels in heaven.

When Jesus says that at the resurrection, people will be like the angels, he cannot mean in every respect. He is narrowing down to the fact that they will not marry (or have sexual relations, presumably) which, far from being bad news, means that they will become like the angels who, being spiritual creatures, do not marry (or engage in sexual activity). Angels relate to one another as do brothers and sisters. This would seem to preclude the idea that the Nephilim of Genesis 6 were heavenly creatures rather than earthly. 

Angels are inferior to Christ but serve as God's messengers

Hebrews 1:4-7 So he became as much superior to the angels as the name he has inherited is superior to theirs. For to which of the angels did God ever say, ‘You are my Son; today I have become your Father’? Or again, ‘I will be his Father, and he will be my Son’? And again, when God brings his firstborn into the world, he says, ‘Let all God’s angels worship him.’ In speaking of the angels he says, ‘He makes his angels spirits, and his servants flames of fire.’ 

Christ's name is superior to that of the angles as although they are referred to as the sons of God at times, he alone is the Son of God. This is fitting because although he was made a little lower than the angels in the incarnation he became as much superior to the angels as the name he has inherited is superior to theirs. The very fact that all the angels worshipped the incarnate Son shows that he is God. (If all were worshipping the Son then none were doing anything else). Angels, in distinction from the Son of God, are like wind and thunder. They are messengers bringing God's message to earth. Like the wind they are invisible and like the lightning they are glorious. They are swift messengers from heaven.

Angels came and attended Jesus tempted in the wilderness

Matthew 4:11 Then the devil left him, and angels came and attended him.

Gill says that these angels came to Jesus in a visible, human form, as they were used to do under the Old Testament dispensation, which seems likely. It happened after the temptation was over; after Satan was foiled, and was gone. The timing shows that Christ alone had got the victory over him, without any help or assistance from the angels. Gill understands them as bringing him food of their own, as with Elijah, (1 Kings 19:5,-8) to satisfy his hunger and refresh him

Thus, says Gill, as the angels are ministering spirits to the heirs of salvation, both in a temporal and in a spiritual sense, (Hebrews 1:14 ) so they were to Christ. Nothing is more frequent with the Jews than to call the angels "ministering angels".

Spurgeon says that the enemy left him when he had shot his last bolt ... for a season .... So soon as the evil one had departed, angels appeared to fulfil a ministry for which they eagerly longed, but which the presence of the devil hindered. No doubt they had been hovering near, waiting their opportunity. These holy beings might not come upon the scene while the battle was being fought, lest they should seem to divide the honours of the day; but when the duel was ended, they hastened to bring food for the body and comfort for the mind of the champion King. It was a battle royal, and the victory deserved to be celebrated by the courtiers of the heavenly King. Let us behold, these angels, learn from their example, and believe that they are also near to all the warriors of the cross in their hour of conflict with the fiend. O Tempted but Triumphant King, thy servants worship thee, and ask permission and grace to minister to thee as angels did!

Mark 1:13 is parallel
and he was in the wilderness forty days, being tempted by Satan. He was with the wild animals, and angels attended him.