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The infrastructure of our modern society is efficient but also sensitive concerningstrong perturbations, as terrorist attacks on the cybersystem or extreme climate events. Animportant part of modern infrastructure are power grids, which are characterized bymultistability. For them, the strongly ongoing transition to distributed renewable energysources leads to a proliferation of dynamical actors. The desynchronization of a few or evenone of those would likely result in a substantial blackout. Thus, the dynamical stability of thewanted synchronous state has become a leading topic in power grid research, in particular forrather strong perturbations where traditional linearization-based concepts are not appropriate.To treat this problem, we firstly discuss the concept of basin stability covering strongperturbations and its estimation even in high-dimensional systems and identify mostvulnerable motifs in power grids. Then additional unwanted dynamics due to lossy cases arepresented.Considering the vulnerability of power grids against extreme wind loads and, consequently,increasing its robustness to withstand these events is of great importance. Here, we combine adetailed model of the climatic drivers of extreme events, and a cascadable model of thetransmission network to provide a holistic co-evolution model to consider wind-inducedfailures of transmission lines in the Texan electrical network. The proposed modellingapproach could be a tool so far missing to effectively strengthen power grids against futurehurricane or typhoon risks even under limited knowledge.