Advantage of CVT - Smooth driving without noticing gear change (Drive by Belt System), low fuel consumption.
Disadvantage of CVT - Cannot use ATF Fluid, must stick with CVT fluid. Life span of CVT gear Box sucks..say 4 to 5 year. then started to judder/jerk when accelerate.
Now u notice that the new Honda City is using 5 speed automatic transmission instead of CVT gear box, because of this problem.