We present recent work on punctuated dynamics of fronts. This kind of
dynamics drives the evolving front to a critical state with temporal m
ultiscaling of the interface profile due to intermittent activity char
acterized by avalanches which connect regions of recent local activity
. This activity pattern exhibits non-trivial power-law correlations in
space and time. We present numerical results in both 1+1 and 2+1 dime
nsions and generalize a theory for the critical exponents to all dimen
sions.