Actuated sensor networks enabled by underwater acoustic communications can be efficiently used to sense over large marine expanses that are typically challenged by a paucity of resources (energy, communication bandwidth, number of sensor nodes). Many marine phenomena of interest admit sparse representations, which, coupled with actuation and cooperation, can compensate for being data starved. Herein, new methods of field reconstruction, target tracking, and exploration-exploitation are provided, which adopt sparse approximation, compressed sensing, and matrix completion algorithms. The needed underlying structure (sparsity/low-rank) is quite general. The unique constraints posed by underwater acoustic communications and vehicle kinematics are explicitly considered. Results show that solutions can be practically implemented, even over large ocean spaces.