Well for a while, the dwarf planet was called a "Moon," but obviously that was changed because you'd have these "moons" far away from any planet.

While one might consider the resource asteroids a kind of moon, they obviously don't look like one and are too small to be anything other than an asteroid caught in the planet's orbit.

I think in order to do justice to the concept of moons, you would have to have them as both close to the planet (as in, within or near its gravity well) and, perhaps most importantly, be substantive additions to gameplay.

At the same time, I seem to remember some kind of memory limit that puts a cap on what the devs can add, so it can't be too much.

So let's have it like this:
A moon would be a structure impervious to damage, much like the capturable resource asteroids that float around asteroid belts. It's model would be a scaled down dwarf planet, not much larger than a dead asteroid. (dwarf planets would be reskinned to something less lunar-like, but only in minor ways. Keep the craters, go for a darker color palette. Maybe have lights from a mining outpost here and there)

On most maps, every player's starting planet would have a moon and certain kinds of planets would randomly have one. Terran and desert would obviously have a high chance for one, with ice and volcanic having a small chance for one. Gas giants would frequently have multiple moons, adding to their importance (I always feel like not enough was done with gas giants).

I think all that sounds fair, right? Reuse assets, mix concepts together (resource asteroids, but in the shape of a dwarf planet), and you'd keep things simple.

But the question of "what do moons do" is less... obvious...
What is clear that, whatever they do, they should have their own Planetary Improvement menu, separate from the main planet.

They could be colonized, but then how does one colonize them? I think having one's starting moon pre-colonized is fair enough, but what about some random world's moon? I'd suppose they'd be colonized seperately from the planet. Perhaps "colonize planet" and "colonize moon" would be seperate ability that share a cooldown timer. Do one and you have to wait in order to do the other. Doing this might make some worlds have a higher tax income than others... which is a touch unfair when you're playing a random map. Maybe have some kind of symmetry? A system will distribute moons randomly, but never lopsided. Certain gravity wells would be more important than others, but only in a strategic sense. You want systems with moons, leading to big battles for them. But what you gain shouldn't be too big, otherwise games would be won in a single engagement. It'd be a king of the hill for the one planet with a moon.

I'd like there to be a way to have, say, a gas giant with many moons, but not all belonging to one player. A sort of stalemate occurs in the gravity well, with both sides' defenses keeping the status quo in play. Perhaps colonizing moons would be a slow process, so that you don't take the entire gravity well in a few minutes and another player can grab one or two for themselves. Yes, I think a slow process would be better. It'd be more of an outpost than a colony.

Which brings me to what I think the best way to have lunar settlements:

You start out with an "outpost," which - much like an unupgraded planet - carries a monetary underdevelopment penalty. The outpost is merely the foundation for whatever might come next, regardless of what shape it takes. Colony (credit source), mining station (slight underdevelopment, but sizable metal and/or crystal income), shipyard, repair station, research station (could count as both military and civic!), fortress (defense > offense), giant cannon (offense > defense), etc. Anything you could imagine being on a moon, you could potentially have. I'm not suggesting which should be implemented, just suggesting.

Each of these would have two or three levels, improving whatever bonus it gives - perhaps with a visual component, such as a colony's lights becoming increasingly numerous as you upgrade it. Just a couple dots or a handful of visible buildings, nothing major.

I would very much like to see a starbase-like structure built around a small planetoid. Would make sieges a lot more interesting if the planet shoots back.

But, defensive fortress excluded, these moon bases would have very little health and are vulnerable to siege frigates and anti-structure units alike. The moon itself is invulnerable, but the colony isn't.

I am tempted to suggest that these moons have unique planetary features, but really that's asking too much. While it'd be fun to have Io or Europa equivalents, the best we could do is a generic moon.

Think that's elaborate enough.