Homelessness represents an enduring public health threat facing communities across the developed world. Children, families, and marginalized adults face life course implications of housing insecurity, while communities struggle to address the extensive array of needs within heterogeneous homeless populations. Trends in homelessness remain stubbornly high despite policy initiatives to end homelessness. A complex systems perspective provides insights into the dynamics underlying coordinated responses to homelessness. A constant demand for housing assistance strains service delivery, while prevention efforts remain inconsistently implemented in most countries. Feedback processes challenge efficient service delivery. A system dynamics model tests assumptions of policy interventions for ending homelessness. Simulations suggest that prevention provides a leverage point within the system; small efficiencies in keeping people housed yield disproportionately large reductions in homelessness. A need exists for policies that ensure reliable delivery of coordinated prevention efforts. A complex systems approach identifies capacities and constraints for sustainably solving homelessness.