Understanding the neurobiological underpinnings of psychiatric disorders has long been a challenge. This talk addresses this issue by exploring how noninvasive neuroimaging, despite its inherent limitations, can be leveraged to anchor psychiatric disorders into neurobiology. Two main challenges in this endeavor are identified, (a) the inherent noise in noninvasive neuroimaging devices and (b) the limited utilization of biophysical models. To tackle the first challenge, we propose the application of Topological Data Analysis (TDA), specifically Mapper, as a novel approach. I present some promising results on how Mapper can capture evoked transitions during tasks, intrinsic transitions during resting states, changes in the landscape or shape associated with psychiatric disorders, and various pharmacological interventions and neuromodulation techniques. I will also highlight a few methodological advances for Mapper that could enhance its applicability in noninvasive neuroimaging studies. Finally, the talk concludes by posing open questions to better understand the neurobiological basis of psychiatric disorders and pave the way for innovative therapeutic strategies.