In recent years, permissionless blockchains have gained significant attention for their ability to secure and provide transparency in transactions. The development of blockchain technology has shifted from cryptocurrency to decentralized finance, benefiting millions of unbanked individuals, and serving as the foundation of Web3, which aims to provide the next generation of the internet with data ownership for users. The rise of NFTs has also helped artists and creative workers to protect their intellectual property and reap the benefits of their work. However, privacy risks associated with permissionless blockchains have become a major concern for individuals and institutions. The role of blockchain in the transition from Web2 to Web3 is crucial, as it is rapidly evolving. As more individuals, institutions, and organizations adopt this technology, it becomes increasingly important to closely monitor the new risks associated with permissionless blockchains and provide updated solutions to mitigate them. This paper endeavors to examine the privacy risks inherent in permissionless blockchains, including Remote Procedure Call (RPC) issues, Ethereum Name Service (ENS), miner extractable value (MEV) bots, on-chain data analysis, data breaches, transaction linking, transaction metadata, and others. The existing solutions to these privacy risks, such as zero-knowledge proofs, ring signatures, Hyperledger Fabric, and stealth addresses, shall be analyzed. Finally, suggestions for the future improvement of privacy solutions in the permissionless blockchain space shall be put forward.