During the last decade we have witnessed a severe change in computing, as processor clock-rates stopped increasing. Thus, the arguable only way to increase processing power is switching to a parallel computing architecture, like the graphics processing unit (GPU). While a GPU offers tremendous processing power, harnessing this power is often difficult. In our research we tackle this issue, providing various components to allow a wider class of algorithms to execute efficiently on the GPU. These efforts include new processing models for dynamic algorithms with various degrees of parallelism, a versatile task scheduler, based on highly efficient work queues which also support dynamic priority scheduling, and efficient dynamic memory management. Our scheduling strategies advance the state-of-the-art algorithms in the field of rendering, visualization, and geometric modeling. In the field of rendering, we provide algorithms that can significantly speed-up image generation, assigning more processing power to the most important image regions. In the field of geometric modeling we provide the first GPU-based grammar evaluation system that can generate and render cities in real-time which otherwise take hours to generate and could not fit into GPU memory. Finally, we show that mesh processing algorithms can be computed significantly faster on the GPU when parallelizing them with advanced scheduling strategies.