The problem of evil, also known as the Riddle of Epicurus, states:
If God is willing to prevent evil, but is not able to
Then He is not omnipotent.
If He is able, but not willing
Then He is malevolent.
If He is both able and willing
Then whence cometh evil.
If He is neither able nor willing
Then why call Him God?
A strong rebuttal is Plantinga's Free Will Defense, which some philosophizing theologians mistakenly believe is irrefutable. Briefly: creatures must decide themselves their behaviours and beliefs. Therefore, omnipotent, omniscient gods can only create worlds where mortals choose their morals. This addresses moral evils, but not natural evils (such as plagues). Plantinga notes the possibility that free, non-human persons cause natural evils.
The problem of evil is not so simple. The evidential problem of evil, proposed by William Rowe, states that the kinds, amounts, and distributions of evil are evidence against almighty Lords. Refutations to this are difficult because they cannot merely describe logically possible scenarios where absolutely good gods co-exist in a Universe shot and besmirched with evil. Arguments must account for evils that actually happen.
