Here is a Wiki article about it, which has some history and some areas of application where it is considered.
Psychedelic therapy - Wikipedia

This article doesn't include ketamine, but many also like to discuss that under this umbrella. That is indeed now legal in the US, some forms and administrations at least, if it's done according to specific regulations and for certain diagnoses (mostly severe depression), usually at clinics that specialize in it. Insurance typically doesn't cover it though for psych purposes. Typically it is administered at a clinic during sessions designed for this but, where I live, there are now organizations that offer it also to be used at home and the therapists' role then is to prepare the client and then help integrate the experience.

The other one that is getting close to ketamine's clinical availability is MDMA which, like ketamine, is often not considered a "classic" psychedelic, but it definitely has strong mind-altering properties. A main area of application it's being considered is PTSD.

Psilocybin (the active ingredient in magic mushrooms) is not legally approved yet for therapy, only via research studies, but there is a lot of research going on in the context of various issues such as depression, anxiety, addictions, eating disorders and more.

The other drugs are even more experimental at least in the US, not used in formal psychotherapy.

Personally, I've tried most of the major psychedelics at some point recreationally, but usually with the intention of exploration, not much to party etc. I've had some good experiences, some less remarkable, and a few more negative in the moment at least, but nothing damaging. I was usually quite careful and methodical with it, but never supervised, except in that retreat outside of the US. I do not have any other formal, solid diagnoses though except generalized anxiety and had addiction and an eating disorder in the past. I must say that simply using psychedelics on my own didn't help my addiction, and once I had a really horrible experience when I mixed mushrooms with high doses of alcohol (okay that was not wise and very scientific for sure), not even during the trip but the days following. The effects of it went away completely, but did also scare me away from psychedelics for years afterward.