  Unparticles ($\U$) interact weakly with particles. The direct signature of
unparticles will be in the form of missing energy. We study constraints on
unparticle interactions using totally invisible decay modes of $Z$, vector
quarkonia $V$ and neutrinos. The constraints on the unparticle interaction
scale $\Lambda_\U$ are very sensitive to the dimension $d_\U$ of the
unparticles. From invisible $Z$ and $V$ decays, we find that with $d_\U$ close
to 1 for vector $\U$, the unparticle scale $\Lambda_\U$ can be more than $10^4$
TeV, and for $d_\U$ around 2, the scale can be lower than one TeV. From
invisible neutrino decays, we find that if $d_\U$ is close to 3/2, the scale
can be more than the Planck mass, but with $d_\U$ around 2 the scale can be as
low as a few hundred GeV. We also study the possibility of using $V (Z)\to
\gamma + \U$ to constrain unparticle interactions, and find that present data
give weak constraints.
