Christ came to establish both an earthly and a spiritual kingdom. This is clear from the prophecies of both the Old and New Testaments. The establishment of the earthly kingdom promised to Israel in the great covenants of the Old Testament, especially the Davidic Covenant (2 Sam. 7) was, however, dependent on the repentance and response of Israel to their Messiah (Joel 2:12-3:21; Acts 3:19-21). Furthermore, these prophecies anticipate both a suffering Savior who must die for His people and for the all nations, and a glorious reign. This often perplexed the Old Testament prophets who saw both and had difficulty reconciling His suffering and glory.
10 As to this salvation, the prophets who prophesied of the grace that would come to you made careful search and inquiry, 11 seeking to know what person or time the Spirit of Christ within them was indicating as He predicted the sufferings of Christ and the glories to follow. 12 It was revealed to them that they were not serving themselves, but you, in these things which now have been announced to you through those who preached the gospel to you by the Holy Spirit sent from heaven— things into which angels long to look. (1 Pet. 1:10-12)
The Old Testament saw two comings like two great mountain peaks in the distance. You can see the two peaks, but not the valley in between. Though the Old Testament prophets spoke of grace being given to Gentiles, they did not understand all that was involved in God saving Gentiles through a suffering Messiah (see Col. 1:26-27). The Old Testament prophets did predict both the suffering (Isa. 53) and glory (Isa. 11) of the Messiah like the two mountain peaks, but they were not able to distinguish that the former would be fulfilled at His first coming and the latter at His second coming.
So, though there is a spiritual kingdom that God is establishing today with Christ seated at God’s right hand, the New Testament also anticipates the return of Christ and the establishment of His reign on earth as seen the book of Revelation and in the gospels like Matthew 24. Before He will reign on earth, a time of unprecedented trouble will come, the Tribulation, which will be culminated by the personal return of Christ who will destroy and remove the wicked and then establish his government on earth for 1000 years. This will then be followed by the eternal estates. See Revelation 19-22.
There are a number of good books that address this. If you have access to them you might try to get a copy of Progressive Dispensationalism, by Blaising and Bock, and Dispensationalism Revised and Expanded, by Charles Ryrie. We would also suggest our series, Studies in Revelation on our web site under “Bible Studies / NT / by book.”