Chewing gums and chewing gum bases which are cud-forming and chewable at mouth temperature contains a multi-block copolymer having at least two repeating sequences of at least two different polymeric blocks having at least three monomer units each. The multi-block copolymer optionally includes linking units and may be formulated to have non-covalent crosslinking between the copolymer chains. The multi-block copolymer is optionally plasticized with a compatible di-block copolymer to function as an elastomer system in the gum base. Characteristics of the multi-block copolymers can be selected to produce gum bases and chewing gums having desired properties. In some cases, chewed cuds formed from the gum bases may exhibit improved removability from environmental surfaces to which they may become undesirably attached.