There have been decades of research trying to identify biomarkers and structural differences in individuals with neuropsychiatric diseases, using imaging (MRI, fMRI), electrical activity (EEG), or serum markers (blood work) . In major depressive disorder for example, there have been associations made with changes in the prefrontal cortex, thalamus, hypothalamus etc. as seen on MRI. However these findings are neither sensitive nor specific, so psychiatric/behavioral disorders such as MDD is still a clinical diagnosis.

I should make the distinction that there are some psychiatric diseases result from structural diseases of the brain. E.g. Alzheimer's disease, Lewy body dementia, Parkinson's disease, all have distinctive findings on MRI and can have psychiatric symptoms. However most people with psychiatric disorders do not have obvious neurological disease that can be identified with imaging.

There is a lot of research and development in the field, and there is a great effort in psychiatry to incorporate objective measurements to validate clinical findings. So our understanding of neuropsychiatric diseases is likely to change dramatically in the coming years, once we develop the tools to understand these disorders better.