Air noise

Blowing through the instrument. Notated with a verbal instruction and perhaps rhythmic notation. Works best with the valves slightly closed, which gives carrying power.
Air noise:

Bangs

Hitting the instrument with the hand or mouthpiece.
Bangs:

Clacks

Clacking with the mouth into the instrument. Some limited pitch changes may be achieved by depressing valves.
Clacks:

Mouthpiece slaps

Either smacking the palm of the hand onto the mouthpiece, or usign an open embouchure and pure tongue into the mouthpiece. Notated with either x-shaped noteheads, or give the pitch and a verbal instruction (if pitched notes are required). By depressing valves, a range of pitches can be produced.
Mouthpiece slaps:

quartertones

Microtones

Intervals smaller than a semitone. Notations vary, but the examples above show a microtonal inflection and a quartertone. Microtones are easy on the trombone.
Microtones:

Multiphonics

Multiphonics are achieved by singing into the instrument while playing. Notate sung notes with small noteheads. Easy and effective on the trombone, although it is hard to sing a note lower in pitch than the one being played.
Multiphonics: