The Angel of the Lord
The identity of the Angel of the Lord (or the Angel of Yahweh) has intrigued believers and scholars for centuries. Let’s walk through what the Bible says.

Key Biblical Evidence about the Angel of the Lord
The Angel of the Lord often speaks as God Himself
Genesis 16:7-13 - The Angel appears to Hagar. In verse 10 , the Angel of the Lord promises, I will multiply thy seed exceedingly - a promise only God can make. In verse 13 , Hagar calls Him Thou God seest me.

Genesis 22:11-18 - The Angel calls to Abraham from heaven, and in verse 12 says, now I know that thou fearest God, seeing thou hast not withheld thy son, thine only son from me. Then in verse 16 He swears by Himself: By myself have I sworn, saith the Lord.

Exodus 3:2-6 - The Angel appears to Moses in the burning bush. Verse 4 says God called unto him out of the midst of the bush, and in verse 6 the speaker identifies Himself: I am the God of thy father, the God of Abraham, the God of Isaac, and the God of Jacob.

The Angel of the Lord accepts worship
When He appears, people often respond in fear and reverence, and no rebuke is given (cf. Joshua 5:13-15 where the Captain of the Lord’s host receives worship).
In contrast, when ordinary angels are worshiped (e.g. Revelation 22:8-9 ), they refuse it, saying, See thou do it not: for I am thy fellowservant.

He exercises divine authority
Judges 6:11-24 - The Angel commissions Gideon, performs miracles, and speaks as the Lord.
Judges 13 - Manoah and his wife meet the Angel of the Lord. They fear they will die because we have seen God ( Judges 13:22 ).

Who is the Angel of the Lord?
Old Testament clues strongly point to this being a pre-incarnate appearance of God - specifically, God the Son ( Jesus Christ ). The Angel of the Lord is distinct from God at times (He is sent by God), yet speaks as God and bears God’s authority. After the incarnation of Christ (New Testament), the Angel of the Lord no longer appears in this way. New Testament angels are always distinct messengers, not receiving worship or speaking as God.
John 1:18 says, No man hath seen God at any time; the only begotten Son, which is in the bosom of the Father, he hath declared him.

This suggests that visible manifestations of God in the Old Testament - like the Angel of the Lord - were appearances of the Son before His birth at Bethlehem.

Alternative views
Some believe the Angel of the Lord is simply a special created angel, but this doesn’t easily explain why He speaks as God, makes divine promises, or accepts worship. Others argue it is God the Father manifesting directly, but scripture teaches God the Father is invisible and not seen by human eyes ( 1 Timothy 6:16 ).

Summary
The Angel of the Lord in the Old Testament is most likely the pre-incarnate Christ - God the Son appearing temporarily in visible form to deliver a message or intervene on behalf of His people.