The Lord was showing the religious leaders and Israel as a whole that they needed a righteousness that exceeded that of the Pharisees (see Matt 5:20). The Sermon on the Mount, which includes this section of the beatitudes, was designed to show the kind of character men need to have a part in the kingdom which ultimately will include God’s millennial reign on earth in the person of the Messiah, the Lord Jesus Himself. There are many issues here, but faith in Christ alone will allow one into the kingdom and only through faithfulness in this life will those in kingdom be able to have a share in Christ’s reign on earth that will occur sometime in the future, after He returns.
For more on this whole subject, I would suggest you check out the studies on Matthew on our web site, especially the one by Matthew Allen on the Kingdom. Also the outline under Matthew is more than a simple outline and gives the basic argument for each section of the book. This too should help.
While we are a part of a heavenly kingdom now, a time is coming when Christ will return and put down a godless world system under the authority of Satan’s man, the beast, and then He will reign on earth a thousand years before the eternal state. One of the promises of the NT is that faithful believers will be able to reign with him and share in his administration. This is part of what Jesus is speaking about in Matthew 5.