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Most works on modeling the conversation history in Conversational Question Answering (CQA) report a single main result on a common CQA benchmark. While existing models show impressive results on CQA leaderboards, it remains unclear whether they are robust to shifts in setting (sometimes to more realistic ones), training data size (e.g. from large to small sets) and domain. In this work, we design and conduct the first large-scale robustness study of history modeling approaches for CQA. We find that high benchmark scores do not necessarily translate to strong robustness, and that various methods can perform extremely differently under different settings. Equipped with the insights from our study, we design a novel prompt-based history modeling approach, and demonstrate its strong robustness across various settings. Our approach is inspired by existing methods that highlight historic answers in the passage. However, instead of highlighting by modifying the passage token embeddings, we add textual prompts directly in the passage text. Our approach is simple, easy-to-plug into practically any model, and highly effective, thus we recommend it as a starting point for future model developers. We also hope that our study and insights will raise awareness to the importance of robustness-focused evaluation, in addition to obtaining high leaderboard scores, leading to better CQA systems.