The sub-synchronous interactions (SSIs) observed in wind power plants have gained attention in recent years. These oscillations are characterised by the diversity of wind power generation types, power grids and power electronic devices. Two pure electrical oscillations, namely induction generator effect (IGE) and sub-synchronous control interaction in wind farms, are firstly discussed on their different characteristics. Particularly, IGE normally falls into the category of sub-synchronous resonance. Then two major types of wind turbines: doubly fed induction generator and permanent magnet synchronous generator with respect to their participations in SSI are reviewed according to the current research status. Several typical analysis and mitigation techniques in existing literature are also expounded in regard to their advantages and disadvantages. Additionally, the research on a grid-connected voltage-source converter in combination with the phase-locked loop, which has caused instability issues including SSI, is briefly introduced. Conclusions are drawn and several perspectives on the future work are presented at the end of this study.