Tremendous advances in computer power and new algorithms enable the solution of very large systems. In this talk, we will present two parallel multigrid implementations to illustrate some of the challenges in current high performance computing. The hierarchical hybrid grid framework enables the solution of linear systems arising from finite element models with more than 10^10 unknowns by a parallel multilevel method running on up to 4000 processors. This is made possible by a special data structure that exploits redundancies in the matrix coefficients and thus saves about an order of magnitude in memory consumption. As a second example we will discuss the ParExPDE framework that uses object oriented techniques and expression templates to hide the details of parallel programming and which achieves excellent scalability on massively parallel computers.