In this talk, I will discuss some examples of sparse signal detection problems in the context of binary outcomes. These will be motivated by examples from next generation sequencing association studies, understanding heterogeneities in large scale networks, and exploring opinion distributions over networks. Moreover, these examples will serve as templates to explore interesting phase transitions present in such studies. In particular, these phase transitions will be aimed at revealing a difference between studies with possibly dependent binary outcomes and Gaussian outcomes. The theoretical developments will be further complemented with numerical results.