This one-day workshop, which is part of the Fall 2025 IDEAL Special Program on High Dimensional and Complex Data Analysis, will explore the interplay between metric embeddings, high-dimensional geometry, and algorithmic problems in data science and theoretical computer science. Topics include geometric and probabilistic methods for understanding metric spaces, embeddings with low distortion, and the implications of high-dimensional phenomena for efficient computation and data representation. The workshop will bring together researchers from mathematics, computer science, and related areas to foster exchange across these connected fields.