What does Christ mean, when he teaches us to pray, ‘Your kingdom come’?

According to Augustine (ACCS), we should not think of this petition as implying that God is not now reigning:

‘“Come”…is to be understood in the sense of “manifested to humanity.” Just as light that is present is absent to the blind or to those who shut their eyes, so the kingdom of God, though it never departs from the earth, yet is absent to those who know nothing about it. To none, however, will ignorance of God’s kingdom be permitted when his Only Begotten comes from heaven. Then he will be recognizable not only by the intellect but visibly as the Man of the Lord to judge the living and the dead.’

Thomas Watson (The Lord’s Prayer):

Negatively,

(a) He does not mean an earthly or political kingdom.  The apostles expected this, Acts 1:6, but they were mistaken.  ‘My kingdom is not of this world’, Jn 18:36.

(b) He does not mean God’s providential kingdom, for this has already come:

Psalm 75:7 (NET) — ‘For God is the judge! He brings one down and exalts another.’

1 Samuel 2:8 (NET) — ‘He lifts the weak from the dust; he raises the poor from the ash heap to seat them with princes and to bestow on them an honored position. The foundations of the earth belong to the Lord, and he has placed the world on them.’

Acts 4:27–28 (NET) — “For indeed both Herod and Pontius Pilate, with the Gentiles and the people of Israel, assembled together in this city against your holy servant Jesus, whom you anointed,28 to do as much as your power and your plan had decided beforehand would happen.”

Positively,

(a) He means God’s kingdom of grace.

(b) He means God’s kingdom of glory.

The second is just an amplification of the first.  They differ not in nature, but in degree.  But we only enter the kingdom of glory by means of the kingdom of grace.

J.I. Packer agrees with this distinction.  In Growing in Christ, he writes that:

‘God’s kingship and his kingdom are different things. The former is a fact of creation, commonly called providence; the latter is a reality of redemption, properly called grace.’

This difference is reflected not in the vocabulary, but in the substance of biblical teaching.  The word ‘kingdom’ is used twice in the Lord’s Prayer: ‘Your kingdom come’ is a prayer for God’s grace to prevail; ‘Yours is the kingdom’ celebrates the fact of his providence over all things.