In an interconnected world, the challenge of maintaining interdependent systems during disasters and disruptive events, such as pandemics, bushfires, cyber-attacks and trade wars is imperative. The critical infrastructure capabilities to be sustained during disasters are many. COVID-19 has demonstrated how a public health threat can fracture the supply chains, including those that underpin digital systems, and degrade the capacity of software and hardware companies. Society must plan for such digital disruptions if it is to survive such shocks.We explore some of the reasons why this is necessary, including the issue of cascading failures, and examines how and in what form more resilient systems might take. This includes consideration of issues such as the need for incentives in order to drive and maintain adoption of resilient technologies, and how such incentives can be created as a natural property of well-conceived systems.We also briefly examine two initiatives that seek to solve some of the harder problems, including security, trustability, independence from energy and communications infrastructure, and the ability to sustain digital capabilities when digital supply chains fail. This remains an open area requiring attention, if society is to improve its resilience to significant shocks.