Q:

What monochrome color schemes have been popular?

There's the classic black-and-white photography, originating from silver-based photography, contemporarily used mostly to bring out shapes, texture or space, or give a "quality" feeling. And there's the brown-and-white sepia, named after the fish-based that has been used to tone photos since late 1800s; nowadays mostly to convey "old" or "timeless" feeling.
What other two-color schemes are currently popular, or have been popular in the past; why did they become popular, what do they convey?

A:

In traditional terms, it breaks down to two major areas: toning and alternative processes.
There were two big reasons for toning. One was simply to create something that was more "organic" than simple black-and-white, in much the same way that sepia or sienna Conté crayons were often preferred to charcoal or graphite for finished drawings. Almost all of the toners used for this purpose were brownish, and though not all actually used sepia, the name covers the whole territory. In these processes, the fully-developed silver print was essentially bleached out and replaced with a dye, not too unlike the way it was done in the Kodachrome and Technicolor processes. These prints tended to outlast improperly-fixed pure silver prints of the time, but staining and fading are still part of the "look", so a grunge overlay helps a lot if you want to make it convincing.
The second reason for toning was permanence. In these processes, the silver in the print is plated with another metal that is less reactive than silver. (Since that has the side-effect of increasing the size of the grains, the original print has to be lower than normal contrast and the print toned until the desired contrast is reached, so it's a bit of a finicky thing to get right.) The colour of the final print depended on the metal being used. Gold toning lent a blue-violet cold tone; platinum and platinum-palladium a warm tone that was distinctly different from sepia; selenium gave you sepia-like darks but with cleaner highlights and blacker deep shadows; rhodium would give you reddish tones (and thus was rather limited as far as subject matter went—not everything looks good in red). All of these processes were created and used primarily to extend the life of the print, and were indicative of photography as fine art. The papers used for these processes tended to be of archival quality as well, with proven naturally-occurring coatings (notably barium hydroxide, or baryta) that are not as brilliantly white as the grounds often used for more casual printing, so digital simulations should be printed on similar papers to look right.
There was more range available using alternative processes to silver/gelatin. Many of the "classics" used in the nineteenth century were also brownish (or faded to become so), like albumen prints or the Van Dyck process. (Van Dyck brown is still available as a pigment for painting.) Perhaps the most identifiably different process was the cyanotype—it hung on until very recently for document copying, and you may be more familiar with the term "blueprint". That used the very dark and powerful blue pigment ferric ferrocyanide (Prussian blue), which made a very thin film of weakly light-sensitive emulsion practical—a few minutes out in the sun would create the exposure, but indoor light had next to no effect at all. You could use just about any pigment you wanted to, but Prussian blue (like its modern counterpart, phthalocyanine blue) can be very dark blue in even the minutest quantities, so it was especially practical in the early days of photography. Like sepia, these alternative processes tend to connote antiquity, but that doesn't mean they can't be fun as well.
It will not do to leave out hand-toning, which is essentially the art of colouring black-and-white prints. It was still a current art when I was young, but even then its main attraction was the built-in nostalgia aspect. In the digital sphere, we no longer have to layer oils or dyes over our prints using cotton swabs; simply layering a colour version of the image (usually with the saturation boosted) over a black-and-white conversion and lowering the opacity will do the trick (although you might want to give an extra blip of red on children's cheeks—that was part of the vocabulary of the process, and "hand-toned" pictures don't look quite right without it).
You can always choose to go for the pop-art look as well. Both offset printing and serigraphy (screen printing) allowed the artist (or art director) to use just about any colour(s) they wanted. Using a visible halftone screen is part of making a convincing rendition. It can be a bit kitschy, but it's an easy way to say "mid-20th Century commercial" if that's what you want to say.

