The following paper aims to investigate what and how are the main privacy-preserving methods applied in the blockchain-based supply chain industry scenario, with a primary focus on the food sector. Recent developments, such as the exordium of cryptocurrencies to increment efficiency, are withal addressed. Overviews of key use cases in industry and research are provided. Numerous blockchain projects, such as VeChain, or multiple others established on well-known infrastructures such as Ethereum or Hyperledger Fabric, are being developed, introducing cryptocurrencies to contribute to a future food supply chain network. Therefore, the motivation of this investigation is to discover how privacy is protected in the field of the food supply chain by the latest developments, such as cryptocurrencies. Do these techniques avail towards a more secure future in the field of the food supply chain from a privacy perspective, or do they introduce additional bottlenecks that could lead to incipient challenges? The principal results and conclusions reveal that proper privacy-preserving techniques exist and have a vigorous connection with the existing applications in the aliment supply chain sector. However, as the magnitude of data grows and the adoption of blockchain becomes very relevant in the supply chain, more focus needs to be attributed to the direction of how privacy is preserved and better methods need to be implemented as the field evolves. In addition, a privacy-preserving model proposal is presented, along with some guidelines and views on the future of this field.