Hot-melt processable adhesive, such as pressure-sensitive-adhesive (PSA) or heat-activatable adhesive, compositions of the present invention possess a broad formulation latitude and adequate cohesive strength after application for use in high performance applications. Hot-melt processable adhesives of the invention comprise at least one block copolymer comprising at least two A blocks and at least one B block. The A and B blocks are derived from monoethylenically unsaturated monomers, which monomers result in saturated polymer backbones without the need for subsequent hydrogenation upon their polymerization. Preferably, the block copolymer is a (meth)acrylate block copolymer.