A fiber or filament which is formed from ingredients comprising (a) at least one fiber-forming thermoplastic polymer and (b) at least one polybrominated anionic styrenic polymer is provided. The polybrominated anionic styrenic polymer has a bromine content of at least about 50 wt %, and a GPC weight average molecular weight in the range of about 5000 to about 40,000, or a GPC weight average molecular weight of at least about 600,000. When the fiber-forming thermoplastic polymer is a polyester, the polybrominated anionic styrenic polymer is present in a flame resistant or flame retardant amount. When the fiber-forming thermoplastic polymer is a polyamide, the polybrominated anionic styrenic polymer is at least about 2 wt % of the fiber or filament. When the fiber-forming thermoplastic polymer is a polyolefin, at least one synergist is present and the polybrominated anionic styrenic polymer is no more than about 15 wt % of the fiber or filament.