Recent developments in tetraquark studies at LHCb

This proceeding presents recent developments in tetraquark studies, with a focus on analyses conducted by the LHCb collaboration. Key highlights include the observation of the $T_{\psi\psi}(6900)$ tetraquark candidate in the di-$J/\psi$ prompt production channel in $p p$ collisions being the first $cc\overline{c}\overline{c}$ exotic candidate. Furthermore, the discovery of the first open flavor tetraquarks, the $T_{\overline{c}\overline{s}0}(2870)^0$ and $T_{\overline{c}\overline{s}1}(2900)^0$ in the $B^+\rightarrow D^+D^-K^+$ decay is reported. This decay does not only provide an excellent environment to study exotic hadrons in the $D^-K^+$ channel, but also gives insight into charmonium(-like) states in the $D^+D^-$ production system. This is also exploited in the $D^{*\pm}D^\mp K^+$ channel where a simultaneous description of the charge conjugate modes provides a fit sensitive to the spin-parity quantum numbers of the resonances. Three new charmonium(-like) states have been confirmed while also measuring their $J^{PC}$ quantum numbers and previously observed tetraquark states in a new production system.