Maybe you have wondered what this phrase, "Times of the Gentiles," means. Paul gives us part of the answer in Romans 11:25. He calls this a "mystery." In the New Testament a "mystery" is not something inscrutable. It is a "family secret." Those of us who are in the family of God can know what it is... and we should know what it is.
According to the Jewish view the "Times of the Gentiles" began in AD 70 with the invasion of Jerusalem by the Romans and the destruction of the temple. It will continue until the Messiah makes His terrifying entrance, leads Israel in conquest over her enemies, establishes His throne in Jerusalem, and begins His glorious reign upon the earth. The Christian view is very close. We believe it began with the crucifixion of Christ and will continue until the Rapture of the church. In other words, according to both views, we are living in the "Times of the Gentiles" right now.
But there is more truth here. Paul exhorts the Roman (Gentile) Christians not to become "conceited." It was easy for them to become "puffed up" thinking that God had rejected the Jews entirely and now they were the favored ones. But Paul calls this "a partial hardening." In other words, God is still dealing with the Jews--just not wholesale. He is still calling out of the Jewish race a people for Himself, just in sparse numbers. There are Jews coming to faith in Christ. Paul was one! There have been many through the years... even today. But, by and large, the numbers of Jews who are coming to Christ are few and far in between. By far the vast majority of those who have been coming to Christ in the last 2000 years have been Gentiles. This will continue until "the full number of Gentiles has come in." In other words, there is a specific number of non-Jewish people who will put their faith in Jesus. God knows exactly what that number is and who those persons are.
Maybe you have seen that series of commercials about "the Heisman House." It is about a fictitious house where all the former winners of the Heisman trophy live together--I presume watching college football games together. Suppose God had a "Salvation House" where all the redeemed live together. Now suppose that there are only two doors into this house. The front door is for the Jews, and the back door is for the Gentiles. Up through the life of Jesus the front door was wide open and back door was almost completely closed. A few Gentiles managed to squeeze through the opening in the back door. But the majority of those who were entering the "Salvation House" were Jews coming through the front door. But sometime after the resurrection things changed. God seemed to reverse things. He closed the front door almost shut. Oh, He left it cracked a little to allow a spattering of Jews to enter. But He flung the back door wide open, allowing a steady stream of Gentiles to come in. We are currently living in the days of "the front door closed, and back door open." But one day the situation will be flipped again. When the "full number of the Gentiles has come" into the house God will close the back door. Then He will throw open the front door once again. This will only last for a short time--I think seven years. At the end of that period God will close BOTH doors and bolt them securely.
Even now I think I can hear that front door creaking on it's hinges. If you have not entered that door by faith, I urge you to do so quickly!