This theme is found throughout Scripture, and links the two Testaments. It is what is now with God's reign of His people and what will come in the future (Psalm 10:16--18; Dan. 2:44; 4:34; Isa. 9:6-7; Matt 3:1-12; 4:23; 24:14; 28:18-20; Luke 11:20; 16:16; 17:21; 22:16-30; John 18:36; Acts 20:25; 28:23-31; Col. 1:13; 28-29; Gal. 3:16; 26-29; Eph. 2:11-18; 3:6-15; Heb. 1:8-14; Rev. 5:9-10; 7:9; 17:14; 19:16).
John the Baptist announced the Kingdom to us with a since of urgency and at the inauguration of Jesus' ministry on earth. It is now in it's beginning and will be fulfilled, as Jesus said, in the future. Thus, it is already running, and there is more to come with Christ's second coming. Exactly what, we do not know, we only have a glimpse that it will be consummated.
Jesus preached the 'Kingdom of Heaven', which is here and is to come (Matt. 3:2; 4:23; 5:3,10,19-20; 6:10; 33; 7:21; 10:7; 13:24-47). The term the Kingdom of Heaven in Mathew is the same thing as the 'Kingdom of God' in the other 3 Gospels. They both mean God's rule and sovereignty. They point to our eternal future and the church today. Matthew used the expression "Kingdom of Heaven" almost exclusively, whereas the other gospels use the term "kingdom of God" The distinction is who the audience was, to the Jew who Matthew wrote too were reluctant to say the name of God because of their high reverence to His name. To the gentiles and Greeks it did not matter. The kingdom of heaven will culminate with our Lord's second coming with a new heaven and a new earth (2 Pet. 3:13-14; Rev. 21-22)
Our task in the church is to proclaim Christ as Lord, His character, righteousness, peace, and joy, all by the Holy Spirit. The "Coming of the Kingdom" in the O.T. meant that a new stage in God's redemptive plan was coming, CHRIST. The meaning for us is our personal identification/relationship to our Lord and Savior! This is our need, to bow to His Lordship for our betterment and growth!