Someone asked me this question and this is my response:
In the beginning God created everything including people and it was good and perfect. The best part about the garden of Eden was the presence of God. Man/woman had a close union together—they were partners with God.
God told them to replenish the earth to multiply and to take dominion. Basically God put them in charge. It all belonged to God but he gave the executive authority or they were fully authorized managers. Please understand that when God puts his word out he does not take it back—that's called integrity. A person of integrity will always, when he/she gives their word, will fulfill their word –even if they get the short end of the stick.
So God told Adam to have dominion, to be the 'manager of all that was created. There are several references in the bible that suggest that Adam's reign on the earth had a time limit, similar to a lease, so until that 'lease is up, Adam has authority.
Now Adam did what is referred to as 'fell'. Actually what Adam did was commit treason against God. The serpent (satan) offered Adam a deal and Adam took that deal. Adam was created with the ability to make choices of his own free will. God wanted love and obedience without force. Think about it in your own life, if you could force someone to loved you then that love would not be genuine and it would be undesired (a person who is honest with themselves know this is true).
Adam made a deal with the devil and as a result satan became his master and the nature of his new master entered the world. Actually what it causes was the absence of God's presence at least in its fullest sense, because really that is what evil is—the absence of good.
So God's word is out man has dominion for a time and that time must run out. Actually satan is ruling through man as he is called the god of this world. So evil exists and God can only do things legally that does not violate his word. His word however immediately promised a savior that would crush the serpent's 'head' or rule and authority. That is why God (Jesus) had to become fully man, so that he could legally enter this world. Anyway long story short Jesus bore man's sins and sicknesses and defeated the devil. All authority was given to him but he immediately delegated that authority to man by saying go into the entire world and preach the gospel.
So man is the culprit and the responsible party. Even natural disasters such as earthquakes can be traced back to something fallen man has done, like destroying massive forests and such.
Now as far as evil things happening, like child abuse, torture etc. it is our responsibility as Christians to use our authority and prayer to help bring and end and healing to these things. If you are concerned more so about a certain evil
(such as child abuse or drug abuse) then maybe it is your purpose to aid others in this area. I believe all in all that it is more important to try to do something about the evil in the world than to continuously reason why it exists and why God allows it, even though the 'why' seems self evident. God is good all the time and he always sticks to his word.