What are birds' bones filled with?

I’ve heard that birds have hollow bones, which are said to make them lighter. But if the spaces in the bones were filled with any sort of water-based fluid, there wouldn’t be much weight reduction, right? So are they full of air? And if so, how does it get there?

Some areas are pneumatized–filled with air pockets; the air is carried there by the blood, I presume.
Some marrow is also present.

Birds’ respiratory systems are structurally and functionally very different from mammalian lungs. In addition to paired lungs, birds also have multiple sets of air sacs that branch off of the trachea and lungs. These air sacs act like bellows to drive air through the bird’s lung in a single direction, as opposed to the back-and-forth movement of air in the mammal lung. The air sacs extend throughout the body of the bird, and are in communication with the bones in a number of areas. So the air gets into the bones via connections with the air sacs. Pictures and description of the system are here.