Continuous variable quantum key distribution (CV-QKD), utilizes continuous variables encoding such as the quadra-ture components of the quantized electromagnetic field and coherent detection decoding, offering good compatibility with the existing telecommunications technology and components. Continuous variable measurement-device-independent QKD (CV-MDI-QKD) can eliminate all the security threats arising from the receiver effectively, the crucial security loophole of CV-QKD implementations. Recently, CV-MDI-QKD has attracted extensive attentions and witnessed rapid progress. Here, we review the achievements that have been made in the field of CV-MDI-QKD, including the basic principle, advancements in theoretical protocols and experimental demonstrations. Finally, we discuss the challenges faced in practical applications and future research directions.

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