A subspace arrangement is a union of a finite number of subspaces of a vector space. We will discuss the importance of subspace arrangements first as mathematical objects and now as a popular class of models for engineering. We will then introduce some of new theoretical results that were motivated from practice. Using these results we will address the computational issue about how to extract subspace arrangements from noisy or corrupted data. Finally we will turn to the importance of subspace arrangements by briefly discussing the connections to sparse representations, manifold learning, etc...