Wang, glad you asked. I have a couple very good reaons for using dumbells vs barbells.
1. Safety - If I run into trouble I can just drop the dumbells on the floor, to the side. With barbells if you have a problem it might fall on your chest or worse yet, your neck.
2. No Spotter - You don't need a spotter (someone to grab the barbell in case of trouble) so you can workout on schedule without having to find someone who's not busy.
3. Better Workout - This is a personal preference. I believe that you can get a better 'focus' on the muscles for each exercise because you can maintain better form with dumbells (form is key to all exercises).
Barbells tend to 'lock-in' or 'fix' certain positions which prevent your hands and arms from making lateral, forward, or backward motions - thereby putting a lot of pressure on ligaments and tendons.
Though I'm not argueing against using a barbell, I have experienced slight tendon tears in my ACT - Acrio Clavicular Tendon which can take a month to heal. With dumbells I don't get this as the weights 'waver' naturally in response to your particular arm length and position.
Also, as an added benefit, because of this 'wavering' motion, you work more of the smaller muscles with dumbells as you correct the 'wavering'.
Note: I DO use the barbell - for squats only.
Other than that it's all dumbells, machines, and cables.
My general dumbell workout:
CHEST - inclined/declined press, inclined/declined flys.
(also cables and chest machines)
BACK - bent-over rows, inclined reverse flys.
(also seated rows, cables, and back machines)
SHOULDERS - seated press, shrugs, front&side extensions.
(also cables and shoulder machines)
BI's & TRI's - dumbell-curls, curl-bar, seated single-dumbell-press.
(also bi/tri machines, rope, cables)
LEGS - no dumbells - use barbell for standing-squats, hack squat machine, leg extension/curl machines, calve press machine.
I vary these exercises from week to week to give my muscles a 'surprise' workout which prevents them from getting too use to the same routine.
I'm getting tired just writing this! LOL