Jesus' frequently uses the words "Kingdom of Heaven," especially in Matthew 13, as in "The Kingdom of Heaven is like..." We should be careful not to be fooled by this. It does not mean "the Kingdom of God when Jesus Christ returns." That is not what Jesus means.
The Kingdom of God or the Kingdom of Heaven is not just a future matter, but also a present reality. It is not on earth right now as a government, in the form of a nation or a kingdom, but the Kingdom of God exists. Colossians 1:13 says that we have already been translated into the Kingdom of the Son of His love. The word translated is better rendered as "transferred." This is not the Protestant idea of "the Kingdom of God is within you," but the Kingdom of God does exist. Notice Matthew 12:28: "But if I cast out demons by the spirit of God, surely the Kingdom of God has come upon you." It was present then in the person of Jesus Christ and working.
Mark 12:34 contains another example: "So when Jesus saw that he answered wisely, He said to him, 'You are not far from the Kingdom of God.' And after that no one dared question Him." In Luke 10, Jesus uses the term in a present-tense situation. The Kingdom of Heaven is something that happens now or can happen now. Jesus is speaking to His disciples, telling them what they are to do when they go out preaching the gospel: "And heal the sick who are there, and say to them, 'The Kingdom of God has come near to you'" (Luke 10:9). This is similar to what He says to the scribe in Luke 17:21: "Nor will they say, 'See here!' Or 'See there!' For indeed the Kingdom of God is among [as it is better translated] you."
These examples show that Jesus taught His disciples that the Kingdom of God or the Kingdom of Heaven exists now, but it is in a different form from what it will be when Jesus returns and sets up His government. When we yield to God, and when we are accepted by Him as His sons and daughters, as it were, we become citizens of the Kingdom of God. In a sense, then, we all are in the Kingdom of God now.
Nevertheless, we are aiming for that future reality when Jesus Christ comes back and sets His throne upon this earth—when all people will stream to Jerusalem to become part of God's Kingdom. The entire Bible looks forward to this time, but there is a present reality of the Kingdom among His sons and daughters. Paul concurs: "Our citizenship is in heaven" (Philippians 3:20); "We are ambassadors for Christ" (II Corinthians 5:20; our allegiance is to Christ, the King of the Kingdom of God); we are "strangers and pilgrims" in a foreign land (I Peter 2:11). Our land is the Kingdom of God. The country we live in is an alien nation. In true members of God's church, the Kingdom of God is already ruling in them. This is what Jesus means when He speaks of the Kingdom of Heaven.
Some scholars want to throw out the word kingdom when it is used this way, feeling that it is a misleading translation. Of course, many of them are Protestants, who look at it from the understanding of "the Kingdom of God is within you." Nonetheless, they believe that the Kingdom of God or the Kingdom of Heaven in Matthew 13 should be rendered the realm, dominion, or reign of God. He is already our King, reigning over us right now.
Another rendering is a word we should all be familiar with—the sovereignty of God. Have we come under the sovereignty of God? Yes, indeed. We did it voluntarily when we accepted Christ as our Savior. So in this sense, we are in the Kingdom of God, and its rules apply to us.
This is what Jesus means in Matthew 13. He is not doing away with the idea that He will return to this earth and set up His government here after putting down all other government's rule, but He is saying, "Those of you whom I have called out are in the Kingdom of Heaven right now—in a spiritual sense—and you have to live by its rules and fight its enemies. So beware! This is what your life in My Kingdom now will be like."