We'll present a variety of recent advances in parallel recursive filtering on the GPU. Recursive filtering is one of the key operations in image processing. It can be used, for example, to invert the effect of convolutions, to enable highest-quality image interpolation and antialiasing for rendering, and in the fastest implementations of image blurring. We'll cover the content of two SIGGRAPH Asia publications. One focuses on how to break the dependency chain to increase the amount of exposed parallelism while minimizing bandwidth requirements. The other describes the first method to enable filtering of infinite input extensions exactly. The resulting algorithms offer a complete solution to recursive filtering on the GPU. Our implementations are available for free in open source.