My friend Nick gave me a couple of old saws that he'd picked up somewhere. These saws with a pistol grip and long, narrow blades are collectively known as compass saws, and are used for making curving cuts that would be impossible with a broad-bladed panel saw. The very narrow bladed ones are generally called keyhole saws. They're seldom used any more, since just about everybody has an electric jigsaw to do the job, but they are still seen in use by guys putting up plasterboard.
The top one I've cleaned up and reshaped the grip very slightly, given it a few coats of shellac, and replaced the old bent and wobbly blade with a 300mm one from a modern plastic-handled Bahco saw. The new blade has seven teeth per inch while the old one has ten or eleven; I'll see how it goes, and if need be I can always recut the teeth finer. It's a tedious job, but not that difficult.
The bottom one's blade is in much better condition, and it just needs to be given a bit of a polish and sharpen. I'll probably clean up the grip as well, though it doesn't really need much.