Due to the freeze on psychedelic research that hit in the late 60's, there's still a ton of research to be done on various psychedelics, especially more esoteric ones like DMT. So if you're looking for peer-reviewed research on medical benefits, in many instances, you just have to wait until the research has been funded and conducted in the first place.

That said, if you want to see what does exist in the medical literature, PubMed or Google Scholar are our go-to databases for published research findings. Many of the studies you'll find in there are pretty jargon-heavy and not meant for the general public, but you can easily go in there and do a keyword search for the compound you're curious about and you'll get a list of things folks have published. Some studies have methodological issues that only research geeks can pick apart and it's still not always possible to say definitively that the findings of a single study are conclusive, but it's a start.

A better option for laypeople can be databases like Erowid or PsychonautWiki, which, though they don't list much in the way of medical research findings, can give you a more accessible glance at the experiences other people have had on a wide variety of psychedelics through the Experience Reports they collect. You can also occasionally find research cited on Wikipedia, though you'll want to follow up with those to make sure they're legit.