Australia is a maritime nation, relying on access to its surrounding oceans for its economy and security. The Royal Australian Navy conducts undersea surveillance to monitor this vital maritime environment and gain insight into activities beneath the ocean's surface. Australia's maritime jurisdiction is vast, with the world's third-largest Economic Exclusion Zone, but its resources are constrained, with only 5% of the United States’ defense budget and navy personnel. Fortunately, advancements in unmanned vehicles and networked sensors can address this disparity by increasing the capacity of Australia's naval fleet at a fraction of the cost of manned platforms. However, current applications of unmanned systems only address simplified scenarios without defining how the plethora of unmanned systems should be applied across the full spectrum of surveillance operations. A new naval fleet architecture must be designed using systems methodologies to integrate unmanned systems into this holistic “system of systems”. Systems engineering, systems architecture, system modeling, system dynamics, operations research, and design for Six Sigma are complementary methodologies with unique techniques to solve this complex problem. This systematic literature review critically analyzed current unmanned systems and the utility of systems methodologies to design their application in undersea surveillance. It contributes insights into the benefits and challenges of unmanned systems in Australia's maritime context, whilst demonstrating shortcomings with the currently disparate application of methodologies to design unmanned fleet architectures. Further research is justified to design an integrated framework of systems methodologies that designs fleet architectures for Australian undersea surveillance.