Hadron Spectroscopy, exotics and $B_c^+$ physics at LHCb

The LHCb experiment is designed to study properties and decays of heavy flavored hadrons produced from $pp$ collisions at the LHC. During Run~1, it has recorded the world's largest data sample of beauty and charm hadrons, enabling precision spectroscopy studies of such particles. Several important results obtained by LHCb, such as the discovery of the first pentaquark states and the first unambiguous determination of the $Z_c(4430)^-$ as an exotic state, have dramatically increased the interest on spectroscopy of heavy hadrons. An overview of the latest LHCb results on the subject, including the discovery of four strange exotic states decaying as $X \to J/\psi \phi$, is presented. LHCb has also made significant contributions to the field of $B_c^+$ physics, the lowest bound state of the heavy flavor $\bar{b}$ and $c$ quarks. A synopsis of the the latest results is given.