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High-dimensional entanglement is a frontier for quantum information science. In this talk, I discuss the concept of entanglement dimensionality, first for two-particle systems and then for multi-particle systems. I first show how to construct criteria for entanglement dimensionality which supersede several well-known ones from the literature . Then, I present methods for how to quantify high-dimensional entanglement using very few measurements. Finally, I explore the multi-particle scenario - where no standard definition of entanglement dimensionality exists. I propose a definition and present a first study on its characterisation and relevance for state-of-the-art experiments.