Psychedelic and entactogenic drugs, once prohibited, are now being decriminalized at the local level and are poised to soon be regulated as medicines by the FDA. With nearly 100 pharmaceutical and biotech companies developing novel therapeutics from these compounds, it is essential to understand their mechanisms and impacts on the human brain. In this dissertation, we first explore the acute effects of psychedelic drugs on human brain dynamics using a computational framework called network control theory. We reveal that LSD and psilocybin decrease the barriers required for state-transitions in the brain, and this effect covaries with more dynamic brain activity. Incorporating anatomical receptor densities, we find that the serotonin 2a receptor is optimally positioned throughout the brain to facilitate this effect. We then show that time-resolved network control analysis can accurately map and simulate the rapidly-evolving dynamics of DMT, a powerful but short-acting psychedelic. Finally, we investigate brain changes associated with MDMA-assisted therapy for PTSD. We find that MDMA-assisted therapy alters brain response to traumatic memories, highlighting several regions of interest in the salience and default mode networks. Overall, this work provides a framework for understanding the acute impacts of psychedelic drugs on human brain dynamics and could potentially be used to harness or predict these effects for future clinical applications.