Dibond seems to gain in popularity, I've seen big prints laminated between Dibond (back) and Acrylic/Plexi (front). I was told that the front is glued to the print with transparent glue. After all is mounted it is cut on a table-circularsaw to final dimension and the edges get a polishing to smooth them out. All sounded like many $$$$$
Currently two ways to to face mount a print to the plexiglass. One is using a seal product called optimount, an optically clear adhesive which is pH neutral. There are several companies that offer this. This would seem to be more archival.
The other is a process called daisec, which uses a thin layer of silicon adhesive between the print and acrylic. This seems to be more common in Europe. Currently I do not think this can be done with inkjet prints, the adhesive dissolves some ink, so it requires a silver halide print.
I've also heard of using Lexan instead of plexi. I guess the advantage would be stronger so a thinner piece would offer similar protection but would be lighter. This is supposedly what Peter Lik is using, but I was told he doesn't face mount, the print is between aluminum and thin Lexan, which works as long as they are framed. (who knows how much sales people really know, but told the same thing in two different galleries of his).
As mentioned by Bernard, I'm not sure how either process affects the archival qualities of the print.