Over the past 10 years, digitization, big data, and technology advancement has had a significant impact on the work done by computer scientists, information scientists, and archivists. Together, each of these groups has contributed to unlock new areas of trans-disciplinary research that are critical for forward progression in the world of big data, while collectively spurring the creation of a new inter-disciplinary field - Computational Archival Science (CAS). Unfortunately, significant gaps exist, including the lack of a comprehensive definition of CAS. This paper closes those gaps by proposing a new, comprehensive definition of Computational Archival Science (CAS) while simultaneously highlighting key big data challenges that exist both in industry and academia. The paper also proposes important areas of future research especially in the context of big data and artificial intelligence.