Solving sparse systems of linear equations is at the heart of many large-scale scientific and engineering problems. Sparse direct methods, which are based on Gaussian elimination, are known to be memory bound and hence are often not 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 provide examples to illustrate why sparse direct methods are important. Then we will discuss the issue of making sparse direct methods efficient. Efficient direct solutions of sparse linear systems involve not only numerical techniques, but may also require knowledge of data structures, graph theory, complexity analysis, and computer architectures. Permuting (or ordering) the rows and columns of a matrix is one of the crucial tasks. We will provide an overview of the ordering problem and discuss some of the myths and facts.