Christian Reconstructionism is also known as Theonomy (Rule by God's law), or Dominion theology. However it is not the same as the New Apostolic Reformation (NAR) dominionism. Confused yet? According to CARM, the leaders of this theology arose out of the conservative Reformed (Calvinist) churches. The leading proponent is Rousas John Rushdoony (1916 - 2001) who in 1973 published the Institutes of Biblical Law, a large work expounding the 10 commandments. Recent advocates are Gary North, Gary DeMar, Kenneth Gentry, Larry Pratt, Greg Bahnsen.
Christian Reconstructionism (also known as theonomy) is a highly controversial movement within some conservative Christian circles. It maintains that the world should be brought under (reconstructed) the lordship of Jesus Christ in all areas: social, moral, political, judicial, military, family, art, education, music, etc. Christian Reconstructionism advocates the restoration of Old Testament civil and moral laws in order to reconstruct present American society into an Old Testament type Mosaic form and that the three main areas of society - family, church, government - should all be biblically modeled, the Bible being the sole standard. This would include severe punishments for law breakers. Some Christian reconstructionists would advocate death for adulterers, abortionists, idolaters, murderers, homosexuals, rapists, etc.
Reconstructionts strongly believe that the Bible is true and inerrant and are generally postmillennial, believing that through the preaching and teaching of the gospel, the world will be converted to Christianity and that Christ will return after a period of time after the world is converted.
Christian reconstructionists believe they are the new chosen people of God, replacing national Israel. Other religious systems would be strongly resisted.
This movement rose out of Calvinism. It is an extremist Christian movement, not held by very many people. Christian reconstructionism began with the publication of the Institute of Biblical Law by R. J. Rushdoony in 1973. This 800 page work expounded on the 10 Commandments. After Rushdoony's death in 2001, his son-in-law Gary North took the reins and has become a prolific writer, further advocating Christian Reconstructionism.
For more, check out this article from Bob DeWaay of Critical Issues Comentary:
The Dominion Mandate and the Christian Reconstruction Movement by Bob DeWaay
A recent theological movement known as Christian Reconstruction has made a significant impact on American Christianity in the past several decades. It is based on a Reformed, Calvinistic view of theology with some significant, unique twists. The most prominent one is the conviction that the Scripture gives the church a mandate to take dominion over this world socially and culturally before the bodily return of Jesus Christ.1 This teaching is known as the “dominion mandate.” Genesis 1:26-28; Genesis 9:1-5 and Matthew 28:18-20 are the principal Biblical passages used to prove the validity of this mandate. The key question to be answered is whether these passages teach the dominion mandate as understood by Christian Reconstructionism. The thesis of this article is that these Biblical passages do not teach a social or cultural domination of the world by Christians before the bodily return of Christ. This issue is important because one's understanding of the Great Commission is at stake. This paper will exegetically examine these passages to prove this thesis. (Read more)