Complex system involves a large number of diverse entities that evolve in a dynamic context. It becomes important for such systems to be able to face this dynamism and respond to different foreseen or unforeseen disruptions in the current industrial, societal and environmental contexts. From our perspective, one can identify different kinds of relevant scientific challenges depending on the time at which the complex system is studied, depending on the occurrences dates of disruptions and depending on the phase of a decision-making process. This paper suggests structuring the different works coping with disruptions in complex systems using a generic framework organized according to the occurrence time of disruptions and on the concerned decision levels in the complex system. Three examples from different areas (health care, physical internet and manufacturing systems) are presented to illustrate the framework. This paper concludes with a set of research prospects.