  We explore the connection between the global symmetry quantum numbers of line
defects and 't Hooft anomalies. Relative to local (point) operators, line
defects may transform projectively under both internal and spacetime
symmetries. This phenomenon is known as symmetry fractionalization, and in
general it signals the presence of certain discrete 't Hooft anomalies. We
describe this in detail in the context of free Maxwell theory in four
dimensions. This understanding allows us to deduce the 't Hooft anomalies of
non-Abelian gauge theories with renormalization group flows into Maxwell theory
by analyzing the fractional quantum numbers of dynamical magnetic monopoles. We
illustrate this method in $SU(2)$ gauge theories with matter fermions in
diverse representations of the gauge group. For adjoint matter, we uncover a
mixed anomaly involving the 0-form and 1-form symmetries, extending previous
results. For $SU(2)$ QCD with fundamental fermions, the 't Hooft anomaly for
the 0-form symmetries that is encoded by the fractionalization patterns of
lines in the Maxwell phase is a consequence of the familiar perturbative
(triangle) anomaly.
