What is the major problem associated with heart transplants today?

A heart transplant is an operation during which a failing or pathological heart is replaced with a healthier, donor heart.Heart transplants are performed once different treatments for heart issues haven't worked.

A heart transplant is not an appropriate option if :

→You're an advanced age that would interfere with the ability to recover       from transplant surgery.
→You have another medical condition that might shorten your   life, despite receiving a donor heart, like a heavy excretory organ, liver   or any respiratory organ.
→You have a serious infection.
→You have a recent personal case history of cancer.
→You are unwilling or unable to create mode changes necessary to       stay your donor heart healthy, like not drinking alcohol or not smoking

The heart surgery carries the risk of many complications like death,bleeding,blood clots and heart attack.
One of the most common risks after having a heart transplant is that your body might reject the donor's heart.
There is also a possibility that the walls of the arteries in your heart could become thicken and harden, which can lead to to cardiac allograft vasculopathy (CAV).

What are the statements?