<p>Our intuition suggests a trend in biological evolution toward greater complexity. However, defining complexity is challenging. Here, we explore measures of biological complexity that assign low complexity to both highly ordered and highly random systems and high complexity to those in between. Most biological systems are highly complex, falling within this intermediate range, displaying both order and variability. Complexity measures quantify the information an organism stores in its genome or nervous system about its environment. Thereby, they support the idea that evolution increases the “knowledge” an organism accumulates about its niche. This is in line with the conceptual framework of cognitive biology, which views evolution as a progressive accumulation of knowledge or as an increase in epistemic complexity. In this view, evolution resembles a cognitive “ratchet” that pushes the organisms unidirectionally towards higher complexity. A dynamic environment continually creates problems to be solved. To survive means to solve problems posed by the environment, and each solution becomes embodied knowledge. Cognitive biology is closely related to the current measures of biological complexity because it uses concepts of information and entropy from information theory and thermodynamics. We also discuss the link between cognitive biology and complexity measures based on integrated information theory (IIT). When considering humans as conscious beings, it seems necessary to postulate the emergence of a new kind of knowledge—self-aware, self-referential knowledge. The appearance of self-reflection in evolution indicates that the human brain and cognition have reached a new qualitative level in epistemic complexity. In summary, cognitive biology, complemented by complexity measures, offers a unified framework for studying the evolution of biological complexity.</p>