Resilience is generally defined as the capacity of a system to recover quickly after shocks. Such an ability for continuity is also relevant for political systems. Important shocks to political systems can be triggered by natural disasters, political regime change, or other major events. We conceptualize political systems as political networks consisting of several interconnected political actors tackling problems on the political agenda. We investigate political networks' ability to recover from shocks. To do so, we first identify different types of shocks that have the ability to impact political networks. Second, we review the literature on resilience and discuss concepts related to political resilience. Third, we outline network measures and models able to grasp the reaction of a political network to shocks, so that we can operationalize the level of resilience of such a system. Throughout the text, we illustrate our theoretical ideas with selected case studies and empirical examples. We conclude that political networks need to allow for change and flexibility during the "after shock" situation: a resilient political network is not one that adopts the exact same shape, but one that has reinforced elements of its structure as a response to a shock. Finally, we outline pathways to future research.