While books have been written on many topics of Polymer Science,no comp- hensive treatise o n l ong-chain b ranching has e ver b een c omposed.This se ries o f reviews in Volume 142 an d 143 o f Advances in P olymer Science tries to fill this gap by highlighting active areas of research on branched polymers. Long-chain branching is a p henomenon observed in s ynthetic polymers and in some natural polysaccharides.It has l ong been r ecognized as a ma jor molecular parameter of macromolecules.Its presence was first surmised by H.Staudinger and G.V.Schulz (Ber.68,2320,1935).Interestingly,their method of identifica- on b y m eans o f the a bnormal r elation b etween in trinsic viscosity an d mo lecular weight has s urvived to this day.Indeed,the most sophisticated method for a- lysis o f long-chain b ranching use s size ex clusion fractionation with the simul- neous recording of mass,molecular weight and intrinsic viscosity of the fr- tions.