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 worlds 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 $Lambda_b^0 to J/psi ppi^-$ mode. The LHCb non-confirmation of the D0 tetraquark candidate in the $B_s^0pi^+$ invariant mass spectrum is presented.
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