The rise of algorithms, Artificial Intelligence, Big Data analysis and the Internet of Things, has the potential to affect fundamental rights in new, yet unfamiliar ways. This paper reviews the consequences of algorithmic-based decision-making for fundamental rights. It does so from the perspective of European fundamental rights law, devoting its attention to four clusters of fundamental rights: (1) privacy (the right to a private life, personal autonomy, human dignity and data protection); (2) equality; (3) freedom (freedom expression, information and religion); and (4) procedural rights. This approach enables the identification of cross-cutting fundamental rights issues and problems, such as the growing relevance of fundamental rights horizontal relations and the exclusionary effects of algorithmic ubiquity. These issues require primary attention when it comes to assessing the potentially damaging effects of the widespread use of algorithms and algorithmic technologies.