The neurobiological mechanisms underpinning psychiatric disorders such as treatment-resistant major depression, post-traumatic stress disorder, and substance use disorders, remain unknown. Psychedelic compounds, such as psilocybin, lysergic acid diethylamide, and N,N-dimethyltryptamine, have emerged as potential therapies for these disorders because of their hypothesized ability to induce neuroplastic effects and alter functional networks in the brain. Yet, the mechanisms underpinning the neurobiological treatment response remain obscure. Quantitative neuroimaging is uniquely positioned to provide insight into the neurobiological mechanisms of these emerging therapies and quantify the patient treatment response. This review aims to synthesize our current state-of-the-art understanding of the functional changes occurring in the brain following psilocybin, lysergic acid diethylamide, or N,N-dimethyltryptamine administration in human participants with fMRI and PET. We further aim to disseminate our understanding of psychedelic compounds as they relate to neuroimaging with the goal of improved diagnostics and treatment of neuropsychiatric illness.