A binder comprising a polymeric binder comprising the products of a carbohydrate reactant and nucleophile is disclosed. The binder is useful for consolidating loosely assembled matter, such as fibers. Fibrous products comprising fibers in contact with a carbohydrate reactant and a nucleophile are also disclosed. The binder composition may be cured to yield a fibrous product comprising fibers bound by a cross-linked polymer. Further disclosed are methods for binding fibers with the carbohydrate reactant and polyamine based binder.