Embedded sensor networks are distributed systems for sensing and in situ processing of spatially and temporally dense data from resource-limited and harsh environments such as seismic zones, ecological contamination sites are battle fields. From an application point of view, many interesting questions arise from sensor network technology that go far beyond the networking/computing aspects of the embedded system. This talk presents an overview of various open problems that are both of mathematical and engineering interests. These problems include sensor-centric quality of routing/energy optimization among other graph theoretic problems.