Data is a precious resource in today's society, and is generated at an unprecedented and constantly growing pace. The need to store, analyze, and make data promptly available to a multitude of users introduces formidable challenges in modern software platforms. These challenges radically transformed all research fields that gravitate around data management and processing, with the introduction of distributed data-intensive systems that offer new programming models and implementation strategies to handle data characteristics such as its volume, the rate at which it is produced, its heterogeneity, and its distribution. Each data-intensive system brings its specific choices in terms of data model, usage assumptions, synchronization, processing strategy, deployment, guarantees in terms of consistency, fault tolerance, ordering. Yet, the problems data-intensive systems face and the solutions they propose are frequently overlapping. This paper proposes a unifying model that dissects the core functionalities of data-intensive systems, and precisely discusses alternative design and implementation strategies, pointing out their assumptions and implications. The model offers a common ground to understand and compare highly heterogeneous solutions, with the potential of fostering cross-fertilization across research communities and advancing the field. We apply our model by classifying tens of systems: an exercise that brings to interesting observations on the current trends in the domain of data-intensive systems and suggests open research directions.