Free will. Much evil is the cost of creatures who genuinely choose, and a world containing free agents is held to be better than a world of automata. This is the most widely used response and it fits moral evil naturally. Critics ask why God could not have created free beings who always in fact choose well, and note how little of natural suffering the answer touches.
Soul-making. Suffering is the condition of moral and spiritual growth; a world without difficulty would produce no character. Irenaeus is its patristic source and John Hick its major modern exponent. Critics answer that suffering destroys at least as often as it develops, and that its distribution bears no relation to who might benefit.
Punishment and desert. Suffering as the consequence of sin is an answer given inside the biblical tradition and explicitly rejected by it: it is what Job's friends say, and they are rebuked for it, and it is what the disciples assume in John 9:2 and are corrected for.
Privation. Evil is not a thing but the absence of a good that should be present, so that God, who creates only being, does not create evil. Augustine took this from Neoplatonism and it became standard in the West. It relieves God of authorship without relieving anyone of suffering, and critics regard it as a solution to a metaphysical problem that leaves the practical one untouched.
Sceptical theism. We are not in a position to judge that any particular evil is gratuitous, since our grasp of the possible goods and their connections is severely limited. Critics reply that the move purchases the defence at the cost of general moral scepticism: if we cannot tell whether an evil is pointless, we cannot tell much else either.
Karma and rebirth. Hindu, Buddhist and Jain thought distributes suffering across a series of lives, which removes the appearance of arbitrariness at a cost that critics inside and outside those traditions have noted, it can appear to hold the sufferer responsible for their suffering. The traditions themselves have contested that implication, and Buddhist writers in particular have insisted that karma explains without licensing indifference.
The refusals. Some of the most serious responses decline to justify at all. The book of Job ends not with an explanation but with an encounter and a series of questions. Post-Holocaust Jewish thought, Richard Rubenstein, Emil Fackenheim, Elie Wiesel, Hans Jonas, treated the classical answers as unusable, and Jonas argued instead for a God who has surrendered power in creating. Process theology denies omnipotence in the traditional sense. Dostoevsky gives the moral objection its sharpest literary form in Ivan Karamazov, who does not deny God but declines to accept a final harmony purchased by the suffering of one child. And the evidential problem remains the strongest argument in the atheist's case. That the discussion has continued for three thousand years without a generally accepted resolution is itself among the more instructive facts about it.