The bark gets tossed on the floor of the wood shed, as a natural mulch. The other small stuff gets tossed into old milk crate-type containers, to be used for kindling.
We just bought one of those outdoor fire pits that you see at Lowes, and HD, and I have found that the small bits are nice for the last few minutes of "happy hour", when I don't intend to be out for long enough to throw more logs on the fire, but want a few more minutes of flames. Bear in mind I am in Florida, so the fires are not usually about warmth, just pyromania.
Larry