Methods of time-parallel time integration have gained increasing interest in the last decade due to the advent of massively parallel computers. We will introduce into the challenges of modern hardware and the problems arising for efficient numerical methods. Constantly increasing parallelism and vectorisation are only accessible with suitable numerical algorithms. One particular approach to introduce sufficient parallel structure in the numerical problem is to use time-parallel (PinT) methods. The time direction then yields additional structure and increases the computational load to take advantage of the available hardware. We introduce the main challenges and ideas and discuss how all-at-one PinT methods can be reformulated into a matrix-fix-point-equation and how these can efficiently be solved with block-Krylov methods, exploiting local parallelism.