At first Glance the Moon Beast is unimpressive, a gray degenerate looking dwarf creature that hops about and flitters its various tentacles blindly. They are nonetheless the natural form of what's known as Illithidae life, and their offshoots have spread stealthily and connivingly across the galaxy, adjacent material reality is something called "potentiality space". This makes a latent presence of Moon Beasts hard to eradicate, as they exist and don't exist in an ephemeral quantum reality of their own making. By and large Moon Beasts live inside moons, and they exist or have existed in most moons of the solar system, and may somehow home in on similar low gravity bodies in the galaxy, and pansmermeate there. Moon Beasts are quick adopters and stealers of technology. Their stuff is a mishmash of stolen technology from literally hundreds of species, much in the same way they organically grow and engineer new bodies from existing other species bodies (i.e. the Illithidea). Moon Beasts are psionic quite versatile and no two Moon Beasts have the same, often quite alien disciplines.
Psychologically and culturally they function as viciously ruthless as, say, Rakka (https://www.youtube.com/watch?v=VjQ2t_yNHQs) and they have no remorse torturing and dissecting live humans. They may easily learn magical ability and those encountered in Dylath Leeen are often necromansers or warlocks by inclination.
In the Dreamlands they seem to have a functional alliance with the Neogi, with which they share many similarities in culture and outlook.