A growing portion of offline and online human activities leave digital footprints in electronic databases. Resulting big social data offers unprecedented insights into population-wide patterns and detailed characteristics of the individuals. The goal of this paper is to review the literature showing how pervasive records of digital footprints, such as Facebook profile, or mobile device logs, can be used to infer personality, a major psychological framework describing differences in individual behavior. We briefly introduce personality and present a range of works focusing on predicting it from digital footprints and conclude with a discussion of the implications of these results in terms of privacy, data ownership, and opportunities for future research in computational social science.