Terpenes are ideal candidates for sustainable polymer feedstocks because of their natural abundance and availability from existing waste streams. Previously, we have shown that a range of terpene(meth)acrylate monomers can be synthesised from the most commonly available terpenes (α-pinene, β-pinenene and limonene) and these readily undergo radical polymerisation. We now report the synthesis of well-defined polymers and precise di- and multiblock copolymer architectures by use of RAFT control. A very wide range of Tg values are observed for the terpene (meth)acrylate homopolymers, from -3 °C for poly(limonene acrylate), up to +168 °C for poly(α-pinene methacrylate), and we exploit these to create renewably-sourced hard-soft block copolymers. We also report the synthesis of difunctional poly(α- and β-pinene methacrylate) macro-RAFT agents and the preparation of ABA triblock copolymers. Promising adhesive properties are observed for a triblock copolymer comprised of poly(α-pinene methacrylate) and poly(butyl acrylate) blocks. A range of fully terpene-based triblock copolymers containing poly(limonene acrylate) soft blocks are also reported.