The possibility to monitor and evaluate power system stability in real-time is in growing demand. Whilst most stability-related studies focus on long-term voltage stability and frequency stability, very little attention is given to the issue of short-term (voltage) instability. In this paper, the most common evaluation methods present in the literature are summarized, with a focus on their applicability to modern power systems with a large amount of renewable energy integration. The paper presents a first-of-a-kind structured review of this topic. We find that all existing methods have noteworthy limitations that necessitate further improvements. Additionally, the need of having an inclusive short-term instability prediction method is demonstrated, due to strong interactions between various short-term instability mechanisms. These findings provide a good foundation for further research and advancement in the field of real-time stability monitoring.