In financial markets, market participants need to cope with risk and uncertainty, to forecast possible scenarios, and to constantly analyze and revise their beliefs, expectations, and strategies in the light of the massive amount of economical and financial information they receive. Interestingly, the relevance does not seem to reside in the numbers itself but rather whether they elicit “surprise” for market participants. In this paper we review the presence of the term surprise in economics and finance as well as how it is computed. Then, we present how emotions are defined in cognitive science, provide a formal definition of surprise, and describe the surprise process. Additionally, we present some theories regarding how artificial surprise can be computed. In a case study we compare the two different perspectives on surprise, discussing some similarities and differences. Finally, we present some possible applications of the cognitive science perspective.