Broadband correlation processing for extracting time-domain Green's functions and coherent wavefronts from random ocean noise has been demonstrated recently using experiments and numerical simulations that are consistent with theoretical predictions. Ocean acoustic noise processing presents additional challenges over its seismological counterpart. Mainly, the ocean environment is temporally non-stationary and it is spatially heterogeneous. Further, in the lower underwater acoustic frequency regime of about 20 to 500 Hz, space-time episodic shipping is the dominant noise source. The data from different publications and research groups are gathered here, with the goal being to review recent underwater acoustic research that demonstrates the viability and potential applications of passive coherent array processing in the ocean.