I'll discuss two research projects involving new directions in irregular problems. The first, called Tarragon, is an actor based programming model to facilitate the design of communication tolerant algorithms, which overlap communication--or I/O--with computation, thereby removing communication from the critical path. I'll discuss the Tarragon programming model, along with some motivating applications and a discussion of load balancing. The second project involves data compression. I'll discuss an algorithm that adaptively coarsens data sets in order reduce their size. Compression ratios of up to an order of magnitude have been observed. The benefit of the technique is that it does not fundamentally change the numerical representation of the original data, thereby enabling the reuse of existing post-processing and analysis software.