The level-set method is one of the most popular techniques for capturing and tracking deformable interfaces. Although level sets have demonstrated great potential in visualization and computer graphics applications, such as surface editing and physically based modeling, their use for interactive simulations has been limited due to the high computational demands involved. In this paper, we address this computational challenge by leveraging the increased computing power of graphics processors, to achieve fast simulations based on level sets. Our efficient, sparse GPU level-set method is substantially faster than other state-of-the-art, parallel approaches on both CPU and GPU hardware. We further investigate its performance through a method for surface reconstruction, based on GPU level sets. Our novel multiresolution method for surface reconstruction from unorganized point clouds compares favorably with recent, existing techniques and other parallel implementations. Finally, we point out that both level-set computations and rendering of level-set surfaces can be performed at interactive rates, even on large volumetric grids. Therefore, many applications based on level sets can benefit from our sparse level-set method.