Despite advancements in deep learning, conversational translation still faces challenges, including ambiguity in short sentences and limited data for colloquial language, as well as the need for culturally-situated and commonsense-based translations. However, Large Language Models (LLMs), using their vast background knowledge, can bring about a fundamental change in conversational translation. Therefore, in this paper, we demonstrate that LLMs, with appropriate prompts, could potentially solve most challenges identified in the last two decades of conversational translation research.