1) Losing something you love. Any time your heart is bound with something else, it hurts to lose it. It doesn't matter if it's a person, a pet, a relationship, or something else you hold dear. The degree of pain may differ, but when the heart hurts it often doesn't differentiate between degrees.
2) Longing for something you can't have. This isn't much different than losing what you love, except that you've never been given the full chance to see that love blossom and grow. You feel in your heart what it could be but know that it won't ever be. The most painful is usually longing for love; whether it's being alone and never finding that special somone, or the ache that comes from wanting and not being able to have children, or even from being in a relationship where love is not readily expressed, the pain can be like a thousand tears forever waiting to fall.
"For all sad words of tongue or pen, the saddest are these 'It might have been'." (John Greenleaf Whittier)
How do you live with unhealed pain? How do you live with regrets? And how can you really regret those things that you would change now with hindsight, but know that to change them would be to deny the good that has also come?
Some losses will never be fully recovered from, some longings will never fade. Somehow we have to pick ourselves up and focus on the vibrancy of the life we've been given. We have the hope of healing through the atonement of Christ. It may not be in this life that the pain is erased, but eventually we will be whole again, and the pain we've felt will be put in perspective. Our joy will outweigh our pain and we will celebrate what our mortal journey was.