Space weather is a collective term for different solar or space phenomena that can detrimentally affect technology. However, current understanding of space weather hazards is still relatively embryonic in comparison to terrestrial natural hazards such as hurricanes or earthquakes. Indeed, certain types of space weather such as large Coronal Mass Ejections (CMEs) are an archetypal example of a low probability, high severity hazard. Few major events, short time-series data and a lack of consensus regarding the potential impacts on critical infrastructure have hampered the economic impact assessment of space weather. Yet, space weather has the potential to disrupt a wide range of Critical National Infrastructure (CNI) systems including electricity transmission, satellite communications and positioning, aviation and rail transportation. Recently there has been growing interest in these potential economic and societal impacts. Estimates range from millions of dollars of equipment damage from the Quebec 1989 event, to some analysts reporting billions of lost dollars in the wider economy from potential future disaster scenarios. Hence, this provides motivation for this article which tracks the origin and development of the socio-economic evaluation of space weather, from 1989 to 2017, and articulates future research directions for the field.