Grid-forming voltage-source converter (GFM-VSC) may experience low-frequency resonances, such as synchronous resonance (SR) and subsynchronous resonance (SSR), in the output power. This article provides a comprehensive study on the low-frequency resonances with GFM-VSC systems and damping control methods. First, the causes of SR and SSR are discussed, highlighting the impacts of control interactions on the resonances. Then, a systematic study of the recent advancements in stabilizing control methods for SR and SSR is presented. Specific physical insights into different damping effects on SR and SSR under weak and stiff grid conditions are revealed and summarized. Furthermore, experimental results comparing the dynamic performances of different damping controls are provided, corroborating the insights obtained in this study. Finally, perspectives on future research trends are shared.