Since its proposition about 2 decades ago, the theory of assessing the brain as a neural network with self-organized criticality has triggered a multitude of research due to its conceptual appeal. Scale-free brain activity as measured by the Hurst exponent (H) of electrophysiological signals and fMRI BOLD signals has been a hallmark of queries related to the ‘criticality hypothesis’ within the field of cognitive neuroscience, which models brain at rest as a network configured to operate near a critical state. In this dissertation I investigated the significance of H in EEG and fMRI data with regards to cognitive processes involved in working memory and learning. In chapter 1, I utilized global H suppression in EEG to distinguish working memory load from cognitive effort. Results from two visual working memory experiments with varying memory set size provided evidence for the suppression of scale-invariance in EEG due to task difficulty that continues even after working memory capacity has been reached. In contrast, task performance and oscillatory signals of working memory load both plateau beyond working memory capacity. This suggests that H suppression may be used to reliably indicate an effortful state. In chapter 2, I used H measured with fMRI data to predict learning in a dual n-back (DNB) working memory task. I hypothesized that learning potential is higher when brain networks are poised closer to a critical state, and thus higher H can be used to predict more learning and improvement on cognitive tasks. The results show that higher H during learning distinguished task improvers from non-improvers. As a comparison, neither baseline task performance nor fMRI functional connectivity strength reliably classified improvers vs. non-improvers. I then successfully cross-validated the H-based model from the DNB dataset on an independent fMRI dataset of participants performing a completely different working memory task (word completion). Taken together, these results suggest that scale-free brain activity can be used as an objective measure of an individual’s cognitive state and provide support for the utility of the criticality hypothesis.