LLMs have become foundational across many NLP applications, driving a shift from an algorithm-centric to a context-centric paradigm. As an important task in text mining, the landscape of topic modeling (TM) is similarly being reshaped by a growing body of LLM-driven research.We review recent TM developments and categorize existing methods into three groups: Classical Algorithm-Centric, LLM-Assisted, and LLM-Centric. For traditional algorithm-centric methods, we refine prior taxonomies and highlight recent advances. For the LLM-Assisted and LLM-Centric settings, we introduce a new taxonomy that emphasizes the role of LLMs and the design of end-to-end workflows, respectively. We examine two key transformations brought by LLM-centric TM: expanded task scope and a shift from model-level improvements to system-level engineering. We also propose a future roadmap for more optimized LLM-Centric TMs and identify ongoing critical challenges. We aim for this survey to spur closer integration between TM and LLMs and to further drive the progress of modern TM.