One of the tricky things about cancers is that they have figured out how to evade the police force of the body, the immune system. The immune system should destroy cancer cells, and yet obviously it doesn't always. How exactly cancer cells figure out how to evade the immune system is something that is being extensively studied. The goal of cancer immunotherapy is to re-train the body's immune system to target and destroy cancer. The best model for this is melanoma, a lethal form of skin cancer. Right now, the best option to treat metastatic melanoma in humans is essentially to infuse patients with IL-2 (the immune equivalent of cocaine-laced red bull) and hope for the best. With IL-2, the body's immune system changes from a local sheriff and his deputies to a full-fledged SWAT team. The immune-swat team still isn't sure what it is hunting for, but it ends up killing a lot, including the cancer if the patient is fortunate. (Giving the swat team specific cancerous targets is the ultimate goal.)
Transplantation immunology is precisely the opposite. Instead of encouraging the immune system to attack the tissue in question, we are doing everything in our power to hold the immune system back. This can be accomplished by drugs which prevent lymphocytes (immune cells) from replicating, block signaling and stimulation, or just kill the lymphocytes outright. Obviously, if the police force is eliminated then a lot of criminals will end up running around; transplant patients are chronically dealing with infections (especially viruses like CMV, HSV, and EBV). Despite these immune-destroying efforts, chronic rejection of transplanted organs by poorly understood mechanisms seems almost inevitable. In humanity's defense, huge strides have been made in dealing with acute transplant rejections, which occur through better understood mechanisms.
It is really interesting if one thinks about it: cancer cells have figured out how to avoid immune destruction, and so the answer to better transplantation immunology is potentially right in front of us and we just can't see it. Another interesting scenario is this: if we took a kidney from a child and transplanted it into the child's mother, the mother would reject the kidney unless appropriate immunosuppressive drugs were given (as in any other case). How then did that child manage to survive in the mother's womb in the first place? Why did the mother's immune system not immediately attack the fetus and destroy it?
The answer is lots of theory backed by some evidence, much of it conflicting. This is the same state of affairs as most other things in medicine. Humility makes a whole lot of sense.