Conversational search facilitates complex information retrieval by enabling multi-turn interactions between users and the system. Supporting such interactions requires a comprehensive understanding of the conversational inputs to formulate a good search query based on historical information. In particular, the search query should include the relevant information from the previous conversation turns.However, current approaches for conversational dense retrieval primarily rely on fine-tuning a pre-trained ad-hoc retriever using the whole conversational search session, which can be lengthy and noisy. Moreover, existing approaches are limited by the amount of manual supervision signals in the existing datasets.To address the aforementioned issues, we propose a **H**istory-**A**ware **Conv**ersational **D**ense **R**etrieval (HAConvDR) system, which incorporates two ideas: context-denoised query reformulation and automatic mining of supervision signals based on the actual impact of historical turns.Experiments on two public conversational search datasets demonstrate the improved history modeling capability of HAConvDR, in particular for long conversations with topic shifts.