The modern clarinet and the modern clarinetist have some of the most advanced technique in the wind world. All members of the clarinet family have identical technique (except for some Contra-Altos and Contrabasses which possess simplified keywork). All clarinets descend to at least a written low E (and the lower clarinets all have at least a semi-tone below this). As for upward range, soprano instruments and lower (except the Contras) should be able to ascend to a written high C (three octaves above middle C), though the practicality of this note might be questioned. The sopranino instruments are best if kept to the G below this high C (four ledger lines above the treble clef), though a few semi-tones higher may be possible. Unfortunately, I cannot vouch for the upper range of the small Piccolo Clarinet, but suffice to say it is probably not possible for them to reach even this high G.
The clarinets that possess a low C extension (F Altos and professional Basses and Contrabasses) have the largest range of any woodwind at a full four octaves.
The only technique limitation on any clarinet is to so-called break. Due to the clarinet’s physics, it does not overblow the octave, but rather the twelfth. This leads to a curious range in between the two main registers where the fingerings can get somewhat awkward. If you are writing for advanced players (high school and above) then you should not have to concern yourself too much with this register and its limitations as the players know how to manage it quite proficiently.
All trills and many tremolos are possible and are quite common.
One curious aspect of the clarinet’s technique that I have alluded to throughout this text is their use of vibrato. In the United States (and in many western European countries) vibrato is not used at all on the clarinet. This makes it the only woodwind instrument in the band to not use the technique. Use this fact to your advantage. Try alternating between the cool vibrato-less pale of the clarinets and the warm vibrato of the saxophones (or flutes or oboes or bassoons). These are curious effects waiting to be explored.
Keep all this in mind and your band won’t be “as bland as B-flat.”