"Because Christ also suffered once for sins, the just for the unjust, to bring you to God, by being put to death in the flesh but by being made alive in the spirit. In it he went and preached to the spirits in prison, after they were disobedient long ago when God patiently waited in the days of Noah as an ark was being constructed."- I Peter 3:18-20
There are a variety of opinions on this question, depending on whether one appeals to modern theologians or the Church Fathers. After considering all of the data, what follows is my understanding of the issue. I have excluded the various heretical ideas proposed by false teachers and Gnostic sects, as these have no apostolic merit whatsoever.
In theology there are necessary implications and potential implications. The verses I quoted from I Peter demand no necessary implications, though there are potential implications. One of the potential implications is that this describes Jesus proclaiming His victory over death to the fallen angels who are bound in the abyss. Personally, I find little evidence to substantiate this position. In fact, most of those who hold this position must appeal to the non-canonical Book of Enoch, or a related philosophy of the "sons of God" mentioned in Genesis 6. As these ideas are not wholly Biblical, and therefore not orthodox, I must reject them.
The other potential implication is that this refers to "Abraham's Bosom"- or Paradise. This position states that those saints who died before the Advent of Christ were not permitted to enter the presence of God, but were sent to Paradise. The problem with accepting this explanation of the Petrine verses in is that it states clearly that the spirits in question were "disobedient". This doesn't seem to support the Paradise position as exclusive to any other position.
The Apostle's Creed says that Jesus "descended into hell". This doesn't mean what most might think it does. The word "hell" is, in Hebrew, the place of the dead- sheol. The equivalent word in Koine Greek is hades. While it is true that Hades is a place of punishment, scripture refers to it as the abode of both the sinful dead and righteous dead. Hades is described as having two separate "sections"; a place of judgment, and a place of blessing.
"And besides all this, between us and you a great chasm has been set in place, so that those who want to go from here to you cannot, nor can anyone cross over from there to us."- Luke 16:26
What did the Church Fathers say on the topic?
"The Lord preached the Gospel to those in Hades...Do not the scriptures show that the Lord preached the Gospel to those who perished in the flood...?"- Clement of Alexandria
"He preached the Gospel to those in the flesh so that they would not be condemned unjustly. So how is it conceivable that He did not for the same reason preach the Gospel to those who had departed this life before His coming?"- Clement of Alexandria
"He preached the Gospel to the souls of the saints.."- Hippolytus
"This was so that He might there make the patriarchs and prophets partakers of Himself."- Tertullian
What emerges from an examination of the Patristic writings is a diversity of opinion, just as we have today in theological circles. So here is my position on this:
Jesus went to the blessed side of Hades (Paradise) and took the souls of the righteous who died before the Atonement to Heaven. It also appears that, while there, He preached to those who died in the flood. Scripture does not indicate whether any of these souls believed or were taken to Heaven. Any statement beyond this would be pure speculation.
I fully admit that my position is potential and not necessary. Therefore, it is certainly open to critique and correction with more Biblical data.