The oval chainring of the late 80's was from Shimano and termed, "Biopace." These fell out of favor due to having the large diameter in the wrong position. This Wikipedia article essentially presents the crux of the Biopace story in the first three paragraphs.
There is now a resurgence of oval chainrings designed differently than Biopace. They are marketed toward mountain and gravel bike riders. Absolute Black and Wolftooth are two leading manufacturers of oval chainrings and both claim abundant research behind their offerings. Their oval (aka: elliptical) chainrings "have the smaller effective chainring diameter coincide with the cranks being at the top dead center (TDC) and bottom dead center (BDC), thus making the crank easier for the rider to turn through bottom dead center for constant chain tension. By having the chainring at its peak effective diameter with the cranks level, where the rider has maximum leverage over the crank during the power stroke, these designs are supposed to make better use of the rider's power output." (Quoted from the above Wikipedia article).
One of the marketing claims is that a 32 tooth oval chainring is like having a 34 tooth ring during the power stroke and a 30 tooth during the part of the pedal stroke where power is not as efficiently applied (the top and bottom dead center). Traction of the rear wheel is improved by creating a situation where there is more consistent torque delivered to the rear wheel. This is helpful in mountain biking and gravel situations where the trail is rock or dirt and may suddenly jut uphill requiring sudden power input on a much lower gear. Users of oval chainrings also tout the benefits to the joints--specifically the knees--because the required force is more equalized through the range of a pedal stroke.
I'm an avid mountain biker, all-mountain/trail single track, and much prefer an oval chainring to round. I use both regularly. You cannot really feel the ovalness of the chainring as you pedal. I can relate that it is easier to clear a difficult technical climb on an oval ring as opposed to a round ring of the same tooth count. The traction seems better as well because I feel I have less spin outs on a given ride with lots of climbing when I'm using an oval chainring.
When I first mounted an oval chainring on my 1x mountain bike, I had also replaced a shifter and switched from resin to metal brake pads and up'd my front rotor from 180mm to 203mm. There was a lot of new things to experience. My first ride while bedding in the pads I was conscious of the new oval chainring. Meaning I paid attention to the feel of the pedal stroke (couldn't tell it wasn't a round ring unless I stared at the rotating ring and observed the subtle forward "bump" of the chain as the oval chainring went around) and the sound of the chain meshing with it. Fast forward a few days of daily riding after work and I had forgotten all about having an oval chainring. Taking a particularly long and difficult ride one day, I was pleasantly surprised and thinking my biking and fitness was really improving as I cleared a couple difficult climbs, one of which I cleared for the first time in maybe a dozen attempts. It wasn't until I was almost home that I remembered I was riding the oval chainring. I believe that made a substantial difference in my performance. That was about three years ago and I've switched out cranksets and spun oval and round rings at different times. While it's possible it's all in my head, I don't think so. I've had a similar experience as I related above except it was disappointment and frustration during a ride in which I was unable to clear a couple climbs that challenge me. Again, it was later in a more relaxed portion of the ride when it occured to me I'd been riding a round ring for a while and wondered if that was the difference. At any rate, this certainly isn't a completely objective assessment, but neither do I feel it's a psychological effect either way.
Overall, I think the oval/elliptical chainrings of today are here to stay. Certainly for the mountain bikers.