  Planck data have been used to provide stringent new constraints on cosmic
strings and other defects. We describe forecasts of the CMB power spectrum
induced by cosmic strings, calculating these from network models and
simulations using line-of-sight Boltzmann solvers. We have studied Nambu-Goto
cosmic strings, as well as field theory strings for which radiative effects are
important, thus spanning the range of theoretical uncertainty in strings
models. We have added the angular power spectrum from strings to that for a
simple adiabatic model, with the extra fraction defined as $f_{10}$ at
multipole $\ell=10$. This parameter has been added to the standard six
parameter fit using COSMOMC with flat priors. For the Nambu-Goto string model,
we have obtained a constraint on the string tension of $G\mu/c^2 < 1.5 x
10^{-7}$ and $f_{10} < 0.015$ at 95% confidence that can be improved to
$G\mu/c^2 < 1.3 x 10^{-7}$ and $f_{10} < 0.010$ on inclusion of high-$\ell$ CMB
data. For the abelian-Higgs field theory model we find, $G\mu_{AH}/c^2 < 3.2 x
10^{-7}$ and $f_{10} < 0.028$. The marginalized likelihoods for $f_{10}$ and in
the $f_{10}$--$\Omega_b h^2$ plane are also presented. We have also obtained
constraints on $f_{10}$ for models with semi-local strings and global textures
for which $G\mu/c^2 < 1.1 x 10^{-6}$. We have made complementarity searches for
the specific non-Gaussian signatures of cosmic strings, calibrating with
all-sky Planck resolution CMB maps generated from networks of
post-recombination strings. We have obtained upper limits on the string tension
at 95% confidence of $G\mu/c^2 < 8.8 x 10^{-7}$ using modal bispectrum
estimation and $G\mu/c^2 < 7.8 x 10^{-7}$ for real space searches with
Minkowski functionals. These are conservative upper bounds because only
post-recombination string contributions have been included in the non-Gaussian
analysis.
