Large scale power failures induced by severe weather have become frequent and damaging in recent years, causing millions of people to be without electricity service for days. Although the power industry has been battling weatherinduced failures for years, it is largely unknown how resilient the energy infrastructure and services really are to severe weather disruptions. What fundamental issues govern the resilience? Can advanced approaches such as modeling and data analytics help industry to go beyond empirical methods? This paper discusses the research to date and open issues related to these questions. The focus is on identifying fundamental challenges and advanced approaches for quantifying resilience. In particular, a first aspect of this problem is how to model large-scale failures, recoveries and impacts, involving the infrastructure, service providers, customers, and weather. A second aspect is how to identify generic vulnerability (i.e., non-resilience) in the infrastructure and services through large-scale data analytics. And, a third is to understand what resilience metrics are needed and how to develop them.