This invention relates generally to anti-Toll-like Receptor 4 (TLR4 antagonists) including antibodies that specifically bind Toll-like Receptor 4 (TLR-4), to methods of using the anti-TLR4 antagonists as therapeutics and to methods of using the anti-TLR4 antagonists for inhibiting, delaying the progression of, or otherwise ameliorating a symptom of Graft-versus-Host disease (GvHD) and/or improving survival of GvHD subjects and/or transplanted biological materials in subjects.