It's true that there is a lot of suffering in the world. Innocent people die frequently. Episodes of great evil such as the Holocaust and genocide seem to be rampant. So how can God allow this all to happen?
I know God does exist, and there are explanations for suffering. Here are some explanations that I have realized as I have thought about the issue:
1. Sometimes we think something that happens is negative only because our perspective is too small.
For one thing, people are so afraid of death that when someone dies, we can often consider that to be the worst possible thing that could happen. But death is not always as bad as we would think. For one thing, our spirits are eternal, and they continue to live after death. All people will be resurrected, through the great resurrection of Jesus Christ. Death scares us, and when a loved one dies we feel sad. But death need not be the end of our existence, nor of our relationships with our loved ones. According to Spencer W. Kimball, "The gospel teaches us there is no tragedy in death, but only in sin."
When the believers in the city of Ammonihah were being burned, Alma and Amulek witnessed the horrible conflagration.
10 And when Amulek saw the pains of the women and children who were consuming in the fire, he also was pained; and he said unto Alma: How can we witness this awful scene? Therefore let us stretch forth our hands, and exercise the power of God which is in us, and save them from the flames. 11 But Alma said unto him: The Spirit constraineth me that I must not stretch forth mine hand; for behold the Lord receiveth them up unto himself, in glory; and he doth suffer that they may do this thing, or that the people may do this thing unto them, according to the hardness of their hearts, that the judgments which he shall exercise upon them in his wrath may be just; and the blood of the innocent shall stand as a witness against them, yea, and cry mightily against them at the last day.
We can trust that God will make sure justice is done. As my dad says, "Life isn't fair, but eternity is."
2. Difficulties and suffering happen to everyone. They are not (necessarily) a punishment from God.
It is true that a person's bad choices can cause suffering for that person. For example, if a person chooses to take drugs, addiction can result, causing the person to lose money, tearing apart that person's relationships, perhaps leading the person into drug trafficking, stealing, etc. These consequences could have been avoided if the person had chosen a better way. But other times our suffering is caused by the poor choices of others. And at still other times suffering seems to be not related to anything we have done.
1 And as Jesus passed by, he saw a man which was blind from his birth. 2 And his disciples asked him, saying, Master, who did sin, this man, or his parents, that he was born blind? 3 Jesus answered, Neither hath this man sinned, nor his parents: but that the works of God should be made manifest in him.
In the case of this story, the man's blindness was not a punishment that either he or his parents had deserved, but rather an opportunity for that man to be a witness to the great healing power of Jesus Christ.
Sometimes things happen that just aren't fair. In the ultimate irony, the Savior Jesus Christ experienced the consequences of the sins and sorrows of the whole world, even though He was One who least deserved punishment for sin. But through this unfair situation, the great Atonement was accomplished which makes it possible for all mankind to be saved. Do we deserve to escape suffering any more than He did?
3. The amount of suffering a person experiences is not a commentary on that person's righteousness.
Two stories from the scriptures that form a good contrast for me are the history of Shadrach, Meschach, and Abednego and the account of Abinadi. In both cases, the person (people) in the story did something righteous which angered a governmental leader and were thrown into a fire as a result. Shadrach, Meschach, and Abednego were miraculously saved from the fire, but Abinadi wasn't. I don't think this means that Abinadi was any less righteous than the three.
4. Difficulties can help to accomplish God's purposes for us.
6 And now when Alma heard this, he turned him about, his face immediately towards him, and he beheld with great joy; for he beheld that their afflictions had truly humbled them, and that they were in a preparation to hear the word.
Sometimes our difficulties can cause us to be humble and seek God. Sometimes it might seem like our difficulties are stopping our progression, when they are actually helping us to progress. Brother S. Michael Wilcox has taught about this scripture in his talk called "When My Prayers Seem Unanswered":
7 And it came to pass that when they were buried in the deep there was no water that could hurt them, their vessels being tight like unto a dish, and also they were tight like unto the ark of Noah; therefore when they were encompassed about by many waters they did cry unto the Lord, and he did bring them forth again upon the top of the waters. 8 And it came to pass that the wind did never cease to blow towards the promised land while they were upon the waters; and thus they were driven forth before the wind.
The same wind that buried the travelers under the water and caused them to cry unto the Lord was the same wind that blew them toward the promised land.
Hugh B. Brown taught this principle in his great talk, "The Currant Bush".
Brigham Young taught:
“Every calamity that can come upon mortal beings will be suffered to come upon the few, to prepare them to enjoy the presence of the Lord. … Every trial and experience you have passed through is necessary for your salvation.” (source)
We don't always know exactly why negative things are happening in life, but we can have faith that God is in charge and that everything has a purpose. As the quote says, "Everything will be okay in the end. If it's not okay, it's not the end." In this beautiful scripture from Revelation, it describes the beautiful experiences we can have after this life:
4 And God shall wipe away all tears from their eyes; and there shall be no more death, neither sorrow, nor crying, neither shall there be any more pain: for the former things are passed away.