This paper reports an overview of recent results in compressive imaging and detection using a single-pixel camera. These applications use a digital micromirror device to spatially modulate the light from an observed scene using binary sensing patterns. The patterns are obtained from a special Hadamard matrix that contains blocks of rows of which each has a common local signature pattern. The blocks partition the Hadamard spectrum, thus permitting analysis of the scene in terms of these local signature patterns. In contrast, Hadamard patterns are typically described in terms of their sequency, which is a global property of each individual row. The proposed local-signature, row-block point of view can be beneficial since it permits us to adaptively select the best blocks with which to sense the signal/scene of interest, or to select the best blocks based on a priori information. As a result, in imaging applications more fine-scale detail can be extracted from the scene, and in detection applications fewer false positives can result. Note, this signature row-block partitioning is a general mathematical technique that can be applied to the Kronecker product of any two matrices, of any size. For example, in our imaging application, we extend this idea to a Hadamard matrix that is not a power of two, yet whose block-signatures possess the familiar Sylvester-Walsh power-of-two sequency patterns.