Inspired by recent advancements in applying Large Language Models for Business Process Management tasks, this keynote reflects on current developments in research and industry in this area. It highlights an evolution from first-wave text-extraction approaches to semantics-aware process analysis and in particular discusses the following directions: (1) moving beyond diverse text-extraction approaches that are hard to compare, by putting a growing emphasis on evaluation rigor (2) using LLMs to support data-driven process analysis by equipping them with a deeper understanding of processes, and (3) increasing the integration of LLMs as semantic connectors and coordinators for solving and supporting process analysis tasks. By focusing on these directions, the keynote aims to foster discussion on the next steps to ensure LLMs create a lasting and meaningful impact in the field of BPM.