In the last two decades, multiple ICT evolutions boosted the ability to collect and analyze vast amounts of data (on the order of Zettabytes). Collectively, they paved the way for the so-called data economy, revolutionizing most sectors of our society, including healthcare, transportation, and grids. At the core of this revolution, distributed data-intensive applications compose services operated by multiple parties in the cloud-edge continuum; they process, manage and exchange massive amounts of data at an unprecedented rate. However, data hold little value without adequate data protection. Traditional solutions, which aim to balance data quality and protection, are insufficient to address the peculiarities of the data economy, including trustworthy data sharing and management, composite service support, and multi-party data life cycle. This article analyzes how trust management systems can regain the lead in supporting trustworthy data-intensive applications, discussing current challenges and proposing a roadmap for new-generation trust management systems in the data economy.