In recent years there has been a resurgence in direct methods to solve linear systems. These methods can have many advantages compared to iterative solvers; in particular their accuracy and performance is less sensitive to the distribution of eigenvalues. However, they typically have a larger computational cost in cases where iterative solvers converge in few iterations. We will discuss a recent trend of methods that address this cost and can make these direct solvers competitive. Techniques involved include hierarchical matrices, hierarchically semi-separable matrices, fast multipole method, etc.