The use of heterogeneous computing resources, such as graphics processing units or other specialized co-processors, has become widespread in recent years because of their performance and energy efficiency advantages. Operating system approaches that are limited to optimizing CPU usage are no longer sufficient for the efficient utilization of systems that comprise diverse resource types. Enabling task preemption on these architectures and migration of tasks between different resource types at run-time is not only key to improving the performance and energy consumption but also to enabling automatic scheduling methods for heterogeneous compute nodes. This thesis proposes novel techniques for run-time management of heterogeneous resources and enabling tasks to migrate between diverse hardware. It provides fundamental work towards future operating systems by discussing implications, limitations, and chances of the heterogeneity and introducing solutions for energy- and performance-efficient run-time systems. Scheduling methods to utilize heterogeneous systems by the use of a centralized scheduler are presented that show benefits over existing approaches in varying case studies.