Literally meaning "large trumpet" (Trombe->Trumpet, One->big), the trombone shares a similar timbre to the trumpet. In the past, the instrument has been used ominously, often signaling evil characters in opera. However, this association is no longer true to the general usage of the instrument.
The range of the tenor trombone can be increased with compensator valves, though the general characterstics shown still apply to the instrument. However, the bass trombone has a similar range to the tuba.
Unlike the other brass instruments, the trombone uses a slide in order to lengthen the instrument. Slide positions enable the player to chromatically descend down to E below the staff (7th position) without the aid of extra tubing. As such, trombones typically do not encounter musical passages with fast scales within ensemble repertoire.
It is common to pair the trumpets and the trombones in modern orchestrations. Due to the lower register, open intervals are recommended, especially in the lower register. Often, in larger groups, trombones are divided into 3 parts (Trombone 1, 2 and Trombone 3/Tuba). As such, the tuba and trombone 3 often reside at the bottom or below the staff, playing the root and the fifth, while the two upper trombones play at the top of the staff.
When writing above the practical range, composers may switch to alto clef. However, due to the skills needed to play in this register (and read alto clef), it is not common to use this within a many ensembles.
The slide enables the use of the signature technique of the trombone. A player may "slide" between 6th and 1st position as indicated at the right for effect. Not all intervals are reasonable for a trombonist to perform. To identify reasonable notes, one note should be in 1st or 2nd position in the trombone's overtone series (shown below) and descend no more than a tritone (1st position only).
Most trombonists will own straight mutes. Jazz trombonists will likely also own plunger, cup, and bucket mutes. Professional musicians may own more. Know your audience. If you write for bucket mute for a community band or church orchestra, there is a good chance the trombones will not own this mute!
While certain brass instruments may be able to quickly change mutes - even while playing - it is even less-practical for the trombone to quickly insert or remove a mute. They use one hand to operate the slide and another to hold the trombone. It is technically possible to perform a mute change on the trombone while playing, but should always be avoided if possible.