The block copolymers according to the invention which are based on conjugated diolefins and polar monomers and are prepared in the presence of catalysts based on the rare earth metals have a high cis-1,4 content in the polydiene block and, because of their polar polymer part and their non-polar diene polymer part, can be used as agents which impart compatibility in the preparation of vulcanizates with a filler content for the production of tires and tire component in the preparation of thermoplastic elastomers or in the modification of thermoplastics.