  We initiate a systematic study of `t Hooft anomalies in Galilean field
theories, focusing on two questions therein. In the first, we consider the
non-relativistic theories obtained from a discrete light-cone quantization
(DLCQ) of a relativistic theory with flavor or gravitational anomalies. We find
that these anomalies survive the DLCQ, becoming mixed flavor/boost or
gravitational/boost anomalies. We also classify the pure Weyl anomalies of
Schr\"odinger theories, which are Galilean conformal field theories (CFTs) with
$z=2$. There are no pure Weyl anomalies in even spacetime dimension, and the
lowest-derivative anomalies in odd dimension are in one-to-one correspondence
with those of a relativistic CFT in one dimension higher. These results
classify many of the anomalies that arise in the field theories dual to string
theory on Schr\"odinger spacetimes.
