Solving sparse systems of linear equations is at the heart of many large-scale scientific and engineering computation.  Sparse direct methods, which are based on Gaussian elimination, are known to be memory bound and hence are often discarded as the methods of choice for large-scale computation.  Yet, they are reliable because they terminate after a finite number of operations.  In this talk, we will consider several common criticisms of sparse Gaussian elimination and comment on their validity.  The talk will touch on several aspects of sparse Gaussian elimination, such as efficiency, data structures, graph theory, complexity analysis, and computer architectures.