Common synthetic fibers

Common synthetic fibers include:

Nylon (1931)
Modacrylic (1949)
Olefin (1949)
Acrylic (1950)
Polyester (1953)
Specialty synthetic fibers include:

Rayon (1894) artificial silk
Vinyon (1939)
Saran (1941)
Spandex (1959)
Vinalon (1939)
Aramids (1961) – known as Nomex, Kevlar and Twaron
Modal (1960’s)
Dyneema/Spectra (1979)
PBI (Polybenzimidazole fiber) (1983)
Sulfar (1983)
Lyocell (1992) (artificial, not synthetic)
PLA (2002)
M-5 (PIPD fiber)
Zylon (PBO fiber)
Vectran (TLCP fiber) made from Vectra LCP polymer
Derclon used in manufacture of rugs

Other synthetic materials used in fibers include:

Acrylonitrile rubber (1930)
Modern fibers that are made from older artificial materials include:

Glass fiber (1938) is used for:
industrial, automotive, and home insulation (glass wool)
reinforcement of composite materials (glass-reinforced plastic, glass fiber reinforced concrete)
specialty papers in battery separators and filtration
Metallic fiber (1946) is used for:
adding metallic properties to clothing for the purpose of fashion (usually made with composite plastic and metal foils)
elimination and prevention of static charge build-up
conducting electricity to transmit information
conduction of heat