It's a leaf miner. There are many different species....but all result in a tiny larva that feeds between the upper and lower leaf surface. If you hold the leaves up to the light, you'll be able see the dark deposits of excrement (frass) and maybe even the larva if it's still present.

Thanks. So these are leaf miners and are apparently hard to kill. Fortunately I don't have mass infestation yet but I'm worried for the spinach that I'm about to plant this fall. I think I'll have to clear out my little balcony garden and clean it big time before planting new stuff :(

Most leaf miner damage is more cosmetic than harmful and most of the controls, pesticides, do more harm than good killing off the predators of the flies that lay the eggs that become the leaf miners.
Floating Row Covers can help keep those adults away so they can't lay those eggs.

Here is a link that might be useful: About Leaf miners

We get those on citrus trees and we control them with a mineral oil and malathion.

Leaf miners need addressed and controlled (if you even choose to control them) before they enter the shelter of the leaf itself and that means the timing of any applications of pesticide need to be pretty precise, unless you are using a systemic and that's something you won't be using for food crops. Many miners are host specific as well and may only target certain plants leaving other ones nearby completely alone. If I have some where it matters to me, it's often controlled simply by removing and discarding the offending leaf.

Malathion is a broad spectrum poison that kills the predators of the flies that lay the eggs that become the leaf miners which then makes the problem even larger.
Plucking off the leaves that have these tunnels may feel good but does little since most often the larva have exited the leaf before you even see their presence. Squishing the leaf between your finders would be more effective if the larva is still present.

It should have been pretty obvious when I said "if you even choose to control them" that plucking off the leaf is an action I'd take for cosmetic reasons to make me feel better.