Urban computing has emerged as a multidisciplinary field that harnesses data-driven technologies to address challenges and improve urban living. Traditional approaches, while beneficial, often face challenges with generalization, scalability, and contextual understanding. The advent of Large Language Models (LLMs) offers transformative potential in this domain. This survey explores the intersection of LLMs and urban computing, emphasizing the impact of LLMs in processing and analyzing urban data, enhancing decision-making, and fostering citizen engagement. We provide a concise overview of the evolution and core technologies of LLMs. Additionally, we survey their applications across key urban domains, such as transportation, public safety, and environmental monitoring, summarizing essential tasks and prior works in various urban contexts, while highlighting LLMs' functional roles and implementation patterns. Building on this, we propose potential LLM-based solutions to address unresolved challenges. To facilitate in-depth research, we compile a list of available datasets and tools applicable to diverse urban scenarios. Finally, we discuss the limitations of current approaches and outline future directions for advancing LLMs in urban computing.