The present invention relates to new, improved or modified polymer materials, membranes, substrates, and the like and to new, improved or modified methods for permanently modifying the physical and/or chemical nature of surfaces of the polymer substrate for a variety of end uses or applications. For example, one improved method uses a carbene and/or nitrene modifier to chemically modify a functionalized polymer to form a chemical species which can chemically react with the surface of a polymer substrate and alter its chemical reactivity. Such method may involve an insertion mechanism to modify the polymer substrate to increase or decrease its surface energy, polarity, hydrophilicity or hydrophobicity, oleophilicity or oleophobicity, and/or the like in order to improve the compatibility of the polymer substrate with, for example, coatings, materials, adjoining layers, and/or the like. Furthermore, this invention can be used to produce chemically modified membranes, fibers, hollow fibers, textiles, and the like, for example, to produce polyolefin microporous battery separators or membranes having improved hydrophilicity or wettability, having crosslinking in the polyolefin which can improve the high temperature stability, and/or the like.