Imagine searching not with keywords, but with flowing conversations. That's the promise of Conversational Search (CS), a field aiming to make information access as natural as chatting with a friend. However, current CS systems face a challenge: balancing accuracy with speed. Large Language Models (LLMs) excel at understanding the nuances of conversation, but using them directly for every search is computationally expensive, leading to annoying delays. New research introduces "DiSCo," a clever approach to distilling the power of LLMs into a faster, more efficient search system. Instead of forcing the search model to mimic the LLM’s internal workings, DiSCo focuses on the end result: the similarity scores between conversations and documents. This "relaxation" of the learning process allows the system to achieve comparable accuracy with far less computational overhead. Experiments show DiSCo significantly improves search relevance, especially in out-of-domain scenarios where the search topics are unfamiliar. The research also explores "multi-teacher distillation," combining insights from multiple LLMs for even better performance. This advancement unlocks faster, more natural search experiences, paving the way for conversational search to become the new standard. Challenges remain in further optimizing efficiency and adapting to the ever-evolving nature of language, but DiSCo presents a key step toward truly conversational information access.