Functions of HLA antigens

Both MHC class I and II are involved in MHC restriction.

Both MHC class I and II are antigens targeted by the immune response in transplant rejection.
Some terms before we proceed:
Graft rejection refers to the recipients immune response rejecting the donor organ.
GVHD (graft versus host disease) refers to the transplanted organ mounting an immune response to the host's antigens. Sounds strange but GVHD is potentially fatal. That is why identification of Ag and Ab in both the recipient and donor is important.

HLA-A, HLA-B and HLA-DR are the main antigens targeted by the recipient, in graft rejection. If there are incompatibilities with these antigens, the feasibility of a successful transplant is low.

All MHC class II antigens are targets in GVHD.

Histocompatibility testing ideally should identify incompatibilities for both class I and class II. This will reduce the likelihood of both graft rejection and GVHD.