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, earthquakes, or tsunamis. 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 the 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. In the early 21st century, 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 asserting that losses will be in the billions of dollars in the wider economy from potential future disaster scenarios. Hence, the origin and development of the socioeconomic evaluation of space weather is tracked, from 1989 to 2017, and future research directions for the field are articulated. Since 1989, many economic analyzes of space weather hazards have often completely overlooked the physical impacts on infrastructure assets and the topology of different infrastructure networks. Moreover, too many studies have relied on qualitative assumptions about the vulnerability of CNI. By modeling both the vulnerability of critical infrastructure and the socioeconomic impacts of failure, the total potential impacts of space weather can be estimated, providing vital information for decision makers in government and industry. Efforts on this subject have historically been relatively piecemeal, which has led to little exploration of model sensitivities, particularly in relation to different assumption sets about infrastructure failure and restoration. Improvements may be expedited in this research area by open-sourcing model code, increasing the existing level of data sharing, and improving multidisciplinary research collaborations between scientists, engineers, and economists.