In one aspect, the present invention provides hydrogels comprising polymer molecules and bridging molecules, wherein substantially all the polymer molecules are cross-linked by hydrogen bonds between polymer molecules and bridging molecules, wherein each bridging molecule is linked to at least two polymer molecules, and wherein there are substantially no covalent linkages between the polymer molecules. In some embodiments, the polymer molecules are poly(vinyl alcohol) (PVA) and the bridging molecules are amino acids. Some embodiments of the invention provide devices comprising hydrogels, and pharmaceutical compositions comprising biologically active molecules within hydrogels. Another aspect provides methods for forming hydrogels of the invention.