Does anybody know anything about the current market or demand for novellas or novelettes? I'm in the beginning stages of my writing career and it looks like, so far, I struggle with being concise enough for short stories but, also, I have yet to put down enough words for a full-on book. I'm curious if pieces in the 25,000 to 45,000 word count range have any place in modern literature. Please say yes.
If you're planning to self-publish, then you would probably have a much better chance of selling your work. Having said that, whether or not you truly find success will depend on how well you write, how ell you promote yourself, and what genre you choose to write in. Some genres, such as romance or erotica, tend to sell a lot of novellas. Some writers have even found success with genres such as mystery/suspense or paranormal. Regardless of your genre, if you write enough of them, and they are written well, then you could find your own level of success.
One of the strategies that I have seen work well for some authors is to write novellas in a series. They will then offer the first book in the series as a freebie or drastically reduced to get readers. If they can get the reader hooked, then the follow-on sales from the other stories in the series can generate some income.
Another strategy is to make one book free or cheap, and then make your profits off of collections. This may be more beneficial if you have more than a couple of stories that are not necessarily part of a series, but at least follow the same specific genre and might appeal to the same readers.
As long as you aren't trying to sell your short work at too high a price then you shouldn't have any problems. I would strongly recommend that your book description include the word count and that you point out that it is a novella or short novel. It is not uncommon for some people to give bad reviews if they were expecting an epic novel but only got a novella.
Novellas don't seem to attract as large of an audience as novels, but they definitely have a place in the market. But if novellas are what you're interested in, definitely go for it! There are several well-known novellas out there, including (but not limited to) The Little Prince, Animal Farm, Three Blind Mice, etc.