ConvSearch-R1 is a pioneering two-stage alignment framework for conversational search that effectively handles conversational query reformulation without the need for external supervised data. It has achieved state-of-the-art performance on the TopiOCQA and QReCC datasets and has been accepted at EMNLP 2025 and the ICML 2025 Workshop. The project is open-sourced with all relevant code, datasets, and models made available for public use.