The "father" of the Dispensationalism theory of understanding the Bible is a former Irish Anglican clergyman named John Nelson Darby (1800 - 1882). In 1830, he began to popularize the belief that that the Church would be raptured away to safety before the Great Tribulation and the return of Jesus Christ. In later years, he used this belief as a springboard to develop a wider Dispensationalism theology.
The theological concept of Dispensationalism got a boost in popularity through the popular Scofield Reference Bible of 1909. The annotated Bible, which focused on prophecy, was the work of a Congregational church pastor named C.I. Scofield (1843 - 1921). In it, Scofield divided God's dealings with mankind into seven distinct dispensations.
The first dispensation entails the time humans were in the Garden of Eden. The second one, called "conscience," centers around man being cast out of Garden due to sin (Genesis 3:23).
The third dispensation begins with God's covenant to Noah not to destroy the earth again through water (Genesis 8:20) and the subsequent start of human governments. The fourth begins when God tells Abram (later Abraham), at the age of 75, to journey to the land of Canaan where he will be made into a great nation (Genesis 12:1 - 3).
The fifth commences when the children of Israel, after leaving Egyptian bondage, agreed to obey God's laws (Exodus 19:8). The sixth dispensation starts with the crucifixion, death, and resurrection of Jesus Christ. The seventh and last 'age' of Dispensationalism constitutes the rule of Christ (Ephesians 1:10).
Unlike replacement theology, which supports the idea that the New Testament Church has completely replaced the physical nation of Israel as God’s chosen people, Dispensationalism states the Eternal is continuing to work with the Jews (despite their rejection of Jesus as the Messiah).
God's dealing with the Jews, according to dispensationalism, will continue up until the Second Coming or (in some versions) during the millennium when Christ rules the earth.
Although Dispensationalism does have some level of truth in it, it tends to go much too far in rejecting God's Old Testament law, which would include laws dealing with sexual morality and murder, in total blanket terms. A radical form of the system claims that all Old Testament law has been completely abolished.