Multidimensional scaling (MDS) extracts meaningful information from pairwise dissimilarity data (e.g., distances between sensors or disagreement scores between individuals) by embedding these relationships into a Euclidean space. However, in practice, the observed dissimilarities are often noisy subject to measurement errors and/or corrupted by noise, but the resulting embeddings are typically interpreted without accounting for this variation. This talk presents recent work on developing a principled statistical framework for MDS. We show that the classical MDS algorithm achieves minimax-optimal performance across a wide range of noise models and loss functions. Building on this, we develop a framework for constructing valid confidence sets for the embedded points obtained via MDS, enabling formal uncertainty quantification for geometric structure inferred from noisy relational data.