From that time Jesus began to preach, and to say, Repent: for the kingdom of heaven is at hand. - Matthew 4:17
But seek ye first the kingdom of God, and his righteousness; and all these things shall be added unto you. - Matthew 6:33
For the kingdom of God is not meat and drink; but righteousness, and peace, and joy in the Holy Ghost. - Romans 14:17
But unto the Son he saith, Thy throne, O God, is for ever and ever: a sceptre of righteousness is the sceptre of thy kingdom. - Hebrews 1:8
For he must reign, till he hath put all enemies under his feet. - I Corinthians 15:25
The above verses present the thought that Jesus Christ established His Kingdom during His first advent, nearly 2000 years ago. Rather than the traditional Jewish view, that the Messiah would reestablish Israel as a nation, rule as King, and dominate the region, Jesus' true Kingdom is one that is a Spiritual Kingdom. Notice the present tense reality of God's Kingdom by the usage of words like is, seek, and reign, all words that indicate a present reality, not a future event.
Through repentance, we enter in to this Kingdom and dwell within it's walls. This Kingdom is to be sought after. Yet, it is not a physical location, but an experience of righteousness, peace, and joy in the Holy Ghost. This is Christ's Kingdom, and He rules over it as Sovereign King. We enjoy the benefits as it's citizens.
But ye are come unto mount Sion, and unto the city of the living God, the heavenly Jerusalem, and to an innumerable company of angel, To the general assembly and church of the firstborn...Wherefore we receiving a kingdom which cannot be moved, let us have grace... Hebrews 12:22-23, 28
From this passage in Hebrews, we safely conclude that the "Kingdom" and "Church" are considered synonymous. I would say, that when everything is as it should be in Christ's Church and you commune with Christ through worship, you have experienced life in the Kingdom.