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This report documents the program and the outcomes of Dagstuhl Seminar "Low-Dimensional Embeddings of High-Dimensional Data: Algorithms and Applications" (24122). Low-dimensional embeddings are widely used for unsupervised data exploration across many scientific fields, from single-cell biology to artificial intelligence. These fields routinely deal with high-dimensional characterization of millions of objects, and the data often contain rich structure with hierarchically organized clusters, progressions, and manifolds. Researchers increasingly use 2D embeddings (t-SNE, UMAP, autoencoders, etc.) to get an intuitive understanding of their data and to generate scientific hypotheses or follow-up analysis plans. With so many scientific insights hinging on these visualizations, it becomes urgent to examine the current state of these techniques mathematically and algorithmically. This Dagstuhl Seminar brought together machine learning researchers working on algorithm development, mathematicians interested in provable guarantees, and practitioners applying embedding methods in biology, chemistry, humanities, social science, etc. The aim of the seminar was to (i) survey the state of the art; (ii) identify critical shortcomings of existing methods; (iii) brainstorm ideas for the next generation of methods; and (iv) forge collaborations to help make these a reality.