The present application provides compositions comprising hyaluronic acid having low levels of functional group modification, mixtures formed by controlled reaction of such lightly modified hyaluronic acid with suitable difunctional or multi-functional crosslinkers, and hydrogel precursor compositions and the resulting hydrogels. The compositions are lightly cross-linked and possess low pro-inflammatory properties when injected in vivo, and can be used as, for example, medical devices, biomedical adhesives and sealants, and for localized delivery of bioactive agents, among other uses.