As computer architectures evolve, numerical algorithms have to cope with high resolution simulations and data integration that are now key to many research fields. Solution methods for real world problems require a constantly increasingly computational effort, demanding for more and more resources and tailored algorithms. 
In this talk we will introduce some recent high-performance algorithmic developments about solving dense linear systems, possibly numerical rank-deficient, and we will present some parallel techniques for the solution of large-scale sparse systems of linear equations.