From Catholicism, here is Fr. Robert Barron on the Problem of Evil.

For the Christian faith, the only adequate resolution of this dilemma is the one affected by God Himself on the cross of Jesus Christ.  On that cross, the darkness of the human condition met the fulness of the Divine Love and found itself transfigured into life.  On that cross, God went to the limits of God-forsakeness and made death itself a place of hope.