The rise of Big, Open and Linked Data (BOLD) enables Big Data Algorithmic Systems (BDAS) which are often based on machine learning , neural networks and other forms of Artificial Intelligence (AI). As such systems are increasingly requested to make decisions that are consequential to individuals, communities and society at large, their failures cannot be tolerated, and they are subject to stringent regulatory and ethical requirements. However, they all rely on data which is not only big, open and linked but varied, dynamic and streamed at high speeds in real-time. Managing such data is challenging. To overcome such challenges and utilize opportunities for BDAS, organizations are increasingly developing advanced data governance capabilities. This paper reviews challenges and approaches to data governance for such systems, and proposes a framework for data governance for trustworthy BDAS. The framework promotes the stewardship of data, processes and algorithms, the controlled opening of data and algorithms to enable external scrutiny, trusted information sharing within and between organizations, risk-based governance, system-level controls, and data control through shared ownership and self-sovereign identities. The framework is based on 13 design principles and is proposed incrementally, for a single organization and multiple networked organizations.