I'm echoing a couple of replies before me, but I'll give concrete examples - MP3, JPEG, and H.264 are all lossy task-specific compressions. Lossless compression includes FLAC and TIFF.

For genetic data, HapZipper beats general-purpose compression. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3488212/

So, yes, actively researched, but you've got to pick a specific task that makes sense. Even small niches are viable; I made a task-specific compressor to strip the essential numbers out of a remote sensor report to make it small enough to squirt to a satellite.