Answer:
Well, there is not really a short answer for it:
1) there are 2 class of MHC:
HLA/MHC-I: binds to CD8 T cells
HLA/MHC-II: binds to CD4 T cells
A physician has to check for a good match of the MHC subtypes in a transplation between graft and host. A good match reduces the risk of immune complications after the transplantation.