  The LHCb experiment is designed to study the decays and properties of heavy
flavoured hadrons produced in the forward region from proton-proton collisions
at the CERN Large Hadron Collider. During Run 1, it has recorded the world's
largest data sample of beauty and charm hadrons, enabling precise studies into
the spectroscopy of such particles, including discoveries of new states and
measurements of their masses, widths and quantum numbers. An overview of recent
LHCb results in the area of exotic hadron spectroscopy is presented, focussing
on the discovery of the first pentaquark states in the $\Lambda_b^0 \to J/\psi
p K^-$ channel and a search for them in the related $\Lambda_b^0 \to J/\psi
p\pi^-$ mode. The LHCb non-confirmation of the D0 tetraquark candidate in the
$B_s^0\pi^+$ invariant mass spectrum is presented.
