Kurzbeschreibung: This talk will be about linear systems and how to solve them. But why should we still think about linear systems? Here are some questions: What if the matrix is too large to load it in memory? What if we never see the full matrix, but only get some rows sequentially? What if we don't have a matrix, but only a program that outputs Ax for a given x, but we can't store enough of the outputs to get a good idea of how the matrix looks like? What if we additionally have a program that evaluates the adjoint, but the adjoint is not exact? How do we even know that the adjoint is wrong? What if we do not want any solution, but need one with specific properties? What if there is no solution, but we still want one? Some of these questions have old answers, some have been answered only recently. Since these are already more questions than I can cover in one lecture, I will make a choice and talk about selected topics.