Blockchain's evolution during the past decade is astonishing: from bitcoin to over 2.000 altcoins, and from decentralised electronic payments to transactions programmable by smart contracts and complex tokens governed by decentralised organisations. While the new generation of blockchain applications is still evolving, blockchain's technical characteristics are also advancing. Yet, immutability, a hitherto indisputable property according to which blockchain data cannot be edited nor deleted, remains the cornerstone of blockchain's security. Nevertheless, blockchain's immutability is being called into question lately in the light of the new erasing requirements imposed by the GDPR's "Right to be Forgotten (RtbF)" provision. As the RtbF obliges blockchain data to be editable in order restricted content redactions, modifications or deletions to be applied when requested, blockchains compliance with the regulation is indeed challenging, if not impracticable. Towards resolving this contradiction, various methods and techniques for mutable blockchains have been proposed in an effort to satisfy regulatory erasing requirements while preserving blockchains' security. To this end, this work aims to provide a comprehensive review on the state-of-the-art research approaches, technical workarounds and advanced cryptographic techniques that have been put forward to resolve this conflict and to discuss their potentials, constraints and limitations when applied in the wild to either permissioned or permissionless blockchains.Index Terms-Blockchain, immutability, Right to be forgotten, GDPR