Studies of complex physical and engineering systems, represented by multi-scale and multi-physics computer simulations have an increasing demand for computing power, especially when the simulations of realistic problems are considered. This demand is driven by the increasing size and complexity of the studied systems or the time constraints. Ultrascale computing systems offer a possible solution to this problem. Future ultrascale systems will be large-scale complex computing systems combining technologies from high performance computing, distributed systems, big data, and cloud computing. Thus, the challenge of developing and programming complex algorithms on these systems is twofold. Firstly, the complex algorithms have to be either developed from scratch, or redesigned in order to yield high performance, while retaining correct functional behaviour. Secondly, ultrascale computing systems impose a number of non-functional cross-cutting concerns, such as fault tolerance or energy consumption, which can significantly impact the deployment of applications on large complex systems. This article discusses the state-of-the-art of programming for current and future large scale systems with an emphasis on complex applications. We derive a number of programming and execution support requirements by studying several computing applications that the authors are currently developing and discuss their potential and necessary upgrades for ultrascale execution.