Complexity science emerged as a transdisciplinary field in the mid-twentieth century, drawing insights from diverse disciplines ranging from physics and biology, mathematics and information theory, as well as the humanities, to develop new understandings of complex systems dynamics. The development of thermodynamics and entropy concepts led to information theory, enabling the study of circular causal feedback loops across social and natural systems. This framework established the foundation for examining how non-linear, path-dependent, recursive dynamics tend towards increases in complexity. Two primary traditions evolved: computational approaches focusing on reductionist analysis, and non-deterministic perspectives studying far-from-equilibrium biological systems. In our own historical moment, postdigital research shares many synergies with complexity science, highlighting and exploring emergent forms of bioinformational complexity as well as new dynamics stemming from mass digitization and information-abundance. This entry traces the historical evolution of complexity science and examines ongoing postdigital challenges in the field.