An efficient overlay is a crucial component of wireless cooperative live video streaming networks—an emerging wireless streaming solution with ever-increasing storage and computation capabilities, and provides scalability, autonomy, carrier-billing network bandwidth conservation, service coverage extension, etc. Based on whether routes are pre-calculated and maintained, or determined per-hop in reactive to each data piece, the streaming overlay can be classified as either unstructured, structured, or hybrid. We discuss issues, properties and example approaches of each category in detail, and present quantitative and qualitative comparisons on their strengths and weaknesses in terms of system robustness, overlay maintenance complexity, delivery ratio, end-to-end delay, etc. Finally we discuss some open issues and emerging areas regarding overlay construction.