  The entrainment transition of coupled random frequency oscillators presents a
long-standing problem in nonlinear physics. The onset of entrainment in
populations of large but finite size exhibits strong sensitivity to
fluctuations in the oscillator density at the synchronizing frequency. This is
the source for the unusual values assumed by the correlation size exponent
$\nu'$. Locally coupled oscillators on a $d$-dimensional lattice exhibit two
types of frequency entrainment: symmetry-breaking at $d > 4$, and aggregation
of compact synchronized domains in three and four dimensions. Various critical
properties of the transition are well captured by finite-size scaling relations
with simple yet unconventional exponent values.
