Software-defined networking (SDN) is an architecture for computer networking that provides a clear separation between network control functions and forwarding operations. The abstractions supported by this architecture are intended to simplify the implementation of several tasks that are critical to network operation, such as routing and network management. Computer networks have an increasingly important societal role, requiring them to be resilient to a range of challenges. Previously, research into network resilience has focused on the mitigation of several types of challenges, such as natural disasters and attacks. Capitalizing on its benefits, including increased programmability and a clearer separation of concerns, significant attention has recently focused on the development of resilience mechanisms that use software-defined networking approaches. In this article, we present a survey that provides a structured overview of the resilience support that currently exists in this important area. We categorize the most recent research on this topic with respect to a number of resilience disciplines. Additionally, we discuss the lessons learned from this investigation, highlight the main challenges faced by SDNs moving forward, and outline the research trends in terms of solutions to mitigate these challenges.