I haven't been satisfied with what I have found in print, as an overview, of this topic ..... the overlapping territory between psychedelic experiences and buddhist practice, so I will get it done myself. All my views are based on first hand personal experience. Other views are those from the one truly qualified teacher of buddhist practice I have met, he was taught personally by the Dalai Lama over decades, and other senior Tibetans he was connected to by the DL. Mine I acquired over four decades of sustained, plodding stepwise effort to master the emotional experiences that have bedeviled and blessed with from quite early in life.
What I say about my experiences will infuriate some folks who will experience it as the rug being yanked on cherished ideas they hold or teachers they have been around ... a few will grin in agreement. I've seen people with impressive sounding higher degrees go temporarily insane, instantly, at the mere suggestion of what I've experienced in a totally unequivocal matter of fact way. That was really shocking to see someone with all the book learning so kookoo.
Surveying the information found online its easy to find lengthy essays quoting personal experience, this historic scholar, that popular well known teacher. I"m always skeptical of lengthy treatments since it does not require a lengthy convoluted explanation, ie deeper meditative states are not a head trip in reality though lots of folks tend to try to turn them into a head trip. Quite the opposite.. And the most interesting and perhaps essential parts is the ineffable, beyond words, and attempts to capture the experience completely automatically reduces it. One can allude to those parts only.
It is well known among people with lots of experience with deeper meditative states, samadhi, vipassana etc that psychedelics, well used, can provide a temporary coarse approximation of a a samadhi like experience. Its also clear one must be very completely clean, clear and free of all substances to get into the real McCoy.
One must also have more up front emotional stability, freedom from agitation and unstable mental emotional states than most westerners have. Psychedelics, well used, can provide an avenue to help acquire the up front mental health in these ways that can put you right at the threshold of moving very quickly into deeper meditative states.
The direct route to Samadhi, in the Tibetan tradition, is a practice called Shamatha. They actually refer to Shamatha not as meditation but as a form of mental training that will make your mind capable of meditation, or Vipassana. When engaged in effective Shamatha practice you will know its working when you have periods that you think you are going insane due to a flow of intense experiences "coming at you" out of the back of your own mind. Prior experiences with psychedelic drugs where you have challenging and similar experiences can be of great help in getting thru it.
It is possible to have these deeper meditative experiences and complete transformation of ones life thru insight or vipassana very quickly with good preparation, great instruction and good motivation. You must learn it from someone who is up to the eyeballs in samadhi ..... that does something profound to your conviction about the process of getting there and the result.
The Tibetans are the only strong direct route I am aware of. Some Zen priests are on to it. American Theravada is in my considerable experiences co-opted, watered down, re packaged to be palatable for and sold to American mainstream. I've never seen anyone go anywhere to speak of in that setting.