In these years, Blockchain technology is growing in importance thanks to cryptocurrencies. This technology offers many features such as the immutability of data stored in the data chain, the replicability of data in nodes, the management without a central repository, etc. These features are widely adopted also in other fields such as in distributed measurement systems. Although the Blockchain technology is widespread worldwide, there is still a legislative gap in the adoption of this technology in various states. This paper will examine the challenge and future trends on distributed measurement systems based on Blockchain technology in the European context. In particular, critical aspects of Blockchain technology will be examined under GDPR point of view and in particular in the management of data and privacy. The advantages and disadvantages of using Blockchain technology in applications such as the Internet of Things and smart contracts will be discussed and some aspects of legal metrology in Blockchain networks will be analyzed. At the end, future trends in Blockchain technology applied to distributed measurement systems will be shown.