<p>Hyperdimensional computing (HDC) is an increasingly popular computing paradigm with immense potential for future intelligent applications. Although the main ideas already took form in the 1990s, HDC recently gained significant attention, especially in the field of machine learning and data science. Next to efficiency, interoperability, and explainability, HDC offers attractive properties for generalization as it can be seen as an attempt to combine connectionist ideas from neural networks with symbolic aspects. While the advantages of HDC have been proven empirically, conceptual motivations behind its representations for machine learning models remain somewhat unclear. The approaches often appear ad hoc engineered, offering limited insight into their possible effectiveness. In recent work, we introduced the hyperdimensional transform, outlining theoretical foundations for representing functions and distributions as high-dimensional holographic vectors. Here, we present the potential of the hyperdimensional transform to a broad data science audience and bridge the gap between the mathematical foundations of the transform and the state-of-the-art HDC approaches for machine learning. Besides providing insight into the current state-of-the-art, we show how the hyperdimensional transform leads to a broad, novel, and well-founded toolbox. Next to the standard regression and classification tasks of machine learning, our discussion includes various aspects of statistical modeling, such as representing, learning and deconvolving distributions, sampling, Bayesian inference, and uncertainty estimation.</p>