There are generally two versions of theodicy in Christendom. The simpler and more popular one can be called the Unknowableness of God Theodicy. It simply states that, for any imaginable theodical problem, God, in His omniscience, can have a perfectly good reason that we just don’t (and can’t at this time) know. And, while this explanation is slightly more satisfying than no explanation, it also creates additional problems. If God is unknowable when it comes to the negative aspects of life, can we really know that He is behind the positives?
The other approach to theodicy is quite a bit more difficult to work through, but, in my opinion, is far more satisfying.
The Free Will approach.
First, contrary to popular opinion, this approach is not: people have free will and suffer because they make poor choices.
Rather, this approach consists of two parts:
1) God initially creates free-willed beings that are sinless. Essentially, they are capable of living harmoniously in a perfect environment where there is no suffering or death.
2) When some of these beings chose to rebel against God’s system, He sets aside a certain period of time allowing them to develop their alternative system, such that, when he finally does bring an end to sin and suffering, no free-willed being will ever want to take that route again. God therefore does not interfere to prevent suffering because, if He did, the flaws of this alternative system would never be fully comprehended by free-willed beings. And, the risk then would be that, once the sin problem is dealt with, it might spring up again.