The article provides a systematic review of the main, existing methodologies of the global monitoring and forecasting of socio-political destabilization. A systematic analysis of the correlation between the forecasts of destabilization generated by these systems and the actual levels of destabilization observed in the respective countries has been carried out. The analysis shows that the forecast, based on the assumption that the level of destabilization in each country in the following year will be proportional to the actual level of destabilization of the current year, turns out, in all cases, to be more predictive than the forecasts made on the basis of any of the considered indices of the risk of destabilization (at least for all cases when the relevant forecasts were published). At the same time, it is shown that, before the Arab Spring, the indices we considered still performed some useful function, allowing us to identify not so much countries with a high risk of destabilization as those countries with particularly low risks of this kind. However, in 2010–2011, all destabilization risk indices had a very serious failure. High index values not only turned out to be not-very-good predictors of a high degree of the actual destabilization in 2011, but also low index values turned out to be bad predictors of a low degree of actual destabilization. As a result, all destabilization risk indices in 2010/2011 showed extremely low statistically-insignificant correlations between the expected and observed levels of destabilization, which can be attributed to the anomalous wave of 2011 launched by the events of the Arab Spring. As we have shown in several ways, the predictive ability of indices had been restored to some extent, again becoming statistically significant after 2011, but it has not returned to the level observed before the Arab Spring. This confirms the conclusions of our previous work that the Arab Spring in 2011 acted as a trigger for the global phase transition, resulting in the World System changing into a qualitatively new state in which we observe some new patterns that were not taken into account by the systems developed before the Arab Spring. Thus, the existing systems of forecasting the risks of socio-political destabilization have lost the last “competitive advantages” over the method of simple extrapolation. There are grounds to believe that the pandemic of the coronavirus infection COVID-19 may lead to an additional decrease in the prognostic ability of the indices we have examined. All this, of course, suggests the need to develop a new generation of systems for forecasting the risks of socio-political destabilization.