  We study the implications of 't Hooft anomaly (i.e. obstruction to gauging)
on conformal field theory, focusing on the case when the global symmetry is
$\mathbb{Z_2}$. Using the modular bootstrap, universal bounds on
(1+1)-dimensional bosonic conformal field theories with an internal
$\mathbb{Z_2}$ global symmetry are derived. The bootstrap bounds depend
dramatically on the 't Hooft anomaly. In particular, there is a universal upper
bound on the lightest $\mathbb{Z_2}$ odd operator if the symmetry is anomalous,
but there is no bound if the symmetry is non-anomalous. In the non-anomalous
case, we find that the lightest $\mathbb{Z_2}$ odd state and the defect ground
state cannot both be arbitrarily heavy. We also consider theories with a $U(1)$
global symmetry, and comment that there is no bound on the lightest $U(1)$
charged operator if the symmetry is non-anomalous.
