Week 5 Muddiest Point

I sure this must have been addressed in the readings somewhere, but I either missed it or the explanation went over my head. I don't quite understand where compression and decompression occurs. Are the programs in charge of this part of the individual OS? Are they in the computer's hardware or in software? Are instructions for "rehydrating" files tacked on to the files themselves somehow, or are they recognizable and assumed by the computer? Sorry to use such remedial language...