The increasing digitalization of contemporary cities has encouraged the adoption of data-centric smart solutions to promote more efficient and sustainable urban governance. Yet, these initiatives often depend on extensive, high-dimensional, and cross-domain datasets, creating difficulties when data quality and availability are limited, and when generating city models and exploring design variations involves substantial costs. Generative Artificial Intelligence (GenAI) has proved as a new deep learning approach for content generation, offering new possibilities for urban science. This paper explores the integration of GenAI with smart city digital twins to enhance the planning and management of critical urban subsystems, including transportation, energy, buildings, and infrastructure. We first introduce state-of-the-art GenAI models, followed by a scoping review of their applications in urban research, operations, and management. Based on this analysis, we identify key opportunities and technical strategies for leveraging GenAI in next-generation smart city digital twins.