The Bible presents divine omniscience as having an all encompassing knowledge about the past, present and future. Elihu calls God "perfect in knowledge" (Job 37:16), and the apostle John writes that God "knows all things" (1 John 3:20). Several Bible verses contribute to the meaning of God's all knowing perfect knowledge.

God's knowledge is infinite.

Great is our Lord and abundant in strength;
His understanding is infinite. (Ps 147:5)

God's knowledge is regarded as beyond any other resource.

Can anyone teach God knowledge,
In that He judges those on high? (Job 21:22)

Who has directed the Spirit of the Lord,
Or as His counselor has informed Him?
With whom did He consult and who gave Him understanding?
And who taught Him in the path of justice and taught Him knowledge
And informed Him of the way of understanding? (Isa 40:13-14)

Omniscience plays an important role in the relationship God has with man; it reflects God's lovingkindness towards His intimate covenant relationship.

Would not God find this out?
For He knows the secrets of the heart. (Ps 44:21)

The Lord knows the thoughts of man,
That they are a mere breath. (Ps 94:11)

O Lord, You have searched me and known me.
You know when I sit down and when I rise up;
You understand my thought from afar.
You scrutinize my path and my lying down,
And are intimately acquainted with all my ways.
Even before there is a word on my tongue,
Behold, O Lord, You know it all.
You have enclosed me behind and before,
And laid Your hand upon me.
Such knowledge is too wonderful for me;
It is too high, I cannot attain to it. (Ps 139:1-6)

So do not be like them; for your Father knows what you need before you ask Him. (Matt 6:8)

With omniscience in view, the grace of God's forgiveness can only be viewed with wonder, because God no longer remembers the sins of a Believer (Heb 10:14-17; Ps 103:11-12). How can the all knowing God forget the sins of a human being?

This too is a reflection of God's covenant relationship and His self proclaimed character of forgiving "iniquity, transgression and sin" yet "by no means leave the guilty unpunished" (Ex 34:6-7). When spoken of God, "remembering" is not understood as the mental act but instead as God's action within the covenant in force.

An example under the Abrahamic Covenant:

Then God remembered Rachel, and God gave heed to her and opened her womb. So she conceived and bore a son and said, "God has taken away my reproach." She named him Joseph, saying, "May the Lord give me another son." (Gen 30:22-24)

An example under the Mosaic Covenant:

How long, O Lord? Will You forget me forever?
How long will You hide Your face from me? (Ps 13:1)

Therefore behold, I will surely forget you and cast you away from My presence, along with the city which I gave you and your fathers. I will put an everlasting reproach on you and an everlasting humiliation which will not be forgotten." (Jer 23:39-40)

An example under the New Covenant:

When divine omniscience includes foreknowledge, there is considerable debate whether it is compatible with the free action of human beings, and this debate has been going on for thousands of years. Regardless, the apostles do not seem to see an incompatibility:

Men of Israel, listen to these words: Jesus the Nazarene, a man attested to you by God with miracles and wonders and signs which God performed through Him in your midst, just as you yourselves know - this Man, delivered over by the predetermined plan and foreknowledge of God, you nailed to a cross by the hands of godless men and put Him to death. (Acts 2:22-23)

Here Peter preaches to the Jews about God's plan of salvation that was prophesized earlier in the Old Testament (Isa 53), which took place through the free action of godless men.

Depending on one's theological perspective, the debate arguments against incompatibility center on clarifying the extent of divine omniscience or the extent of a human being's free will.