Inspired by the $T_{cc}^{+}$ signal discovered by the LHCb Collaboration, we systematically investigate the doubly heavy tetraquark states with the molecule configuration $[Q_1{\overline{q}}_2{]}_{{\mathbf{1}}_c}[Q_3{\overline{q}}_4{]}_{{\mathbf{1}}_c}$ ($Q=c$ and $b$, $q=u$, $d$, and $s$) in a nonrelativistic quark model. The model involves a color screening confinement potential, meson-exchange interactions, and one-gluon-exchange interactions. The state $T_{cc}^{+}$ with $I{J}^P=01^{+}$ is a very loosely bound deuteronlike state with a binding energy around 0.34 MeV and a huge size of 4.32 fm. Both the meson exchange force and the coupled channel effect play a pivotal role. Without the meson exchange force, there does not exist the $T_{cc}^{+}$ molecular state. In strong contrast, the QCD valence bond forms clearly in the $T_{bb}^{-}$ system when we turn off the meson-exchange force, which is very similar to the hydrogen molecule in QED. Moreover, the $T_{bb}^{-}$ becomes a heliumlike QCD-atom if we increase the bottom quark mass by a factor of three. Especially, the states $T_{bb}^{-}$ with ${01}^{+}$, $T_{bc}^0$ with ${00}^{+}$ and ${01}^{+}$, and the $V$-spin antisymmetric states $T_{bbs}^{-}$ with $\frac{1}{2}{1}^{+}$, $T_{bcs}^0$ with $\frac{1}{2}{0}^{+}$ and $\frac{1}{2}{1}^{+}$ can form a compact, hydrogen moleculelike or deuteronlike bound state with different binding dynamics. The high-spin states $T_{bc}^0$ with ${02}^{+}$ and $T_{bcs}^0$ with $\frac{1}{2}{2}^{+}$ can decay into $D$-wave $\overline{B}D$ and ${\overline{B}}_{s}D$ although they are below the thresholds ${\overline{B}}^{*}{D}^{*}$ and ${\overline{B}}_s^{*}{D}^{*}$, respectively. The isospin and $V$-spin symmetric states are unbound. We also calculate their magnetic moments and axial charges.

We use a color-magnetic interaction model (CMIM), a traditional constituent quark model and a multiquark color flux-tube model to systematically investigate the properties of the states $[Q_1{Q}_2][{\overline{Q}}_3{\overline{Q}}_4]$ ($Q=c$, $b$). The dynamical investigation indicates that the CMIM can not completely absorb QCD dynamical effects through the effective constituent quark mass and overestimates the color-magnetic interaction in the states under the assumption of the same spatial configurations. The Coulomb interaction plays a critical role in the dynamical model calculations on the heavy hadrons, which induces the fact that none of bound states $[Q_1{Q}_2][{\overline{Q}}_3{\overline{Q}}_4]$ can be found in the dynamical models. The color configuration ${[[Q_1{Q}_2{]}_{{\mathbf{6}}_c}[{\overline{Q}}_3{\overline{Q}}_4{]}_{{\overline{\mathbf{6}}}_c}]}_{\mathbf{1}}$ should be taken seriously in the ground states due to the strong Coulomb attraction between the $[Q_1{Q}_2{]}_{{\mathbf{6}}_c}$ and $[{\overline{Q}}_3{\overline{Q}}_4{]}_{{\overline{\mathbf{6}}}_c}$. The color configuration ${[[Q_1{Q}_2{]}_{{\overline{\mathbf{3}}}_c}[{\overline{Q}}_2{\overline{Q}}_4{]}_{{\mathbf{3}}_c}]}_{\mathbf{1}}$ is absolutely dominant in the excited states because of the strong Coulomb attraction within the $[Q_1{Q}_2{]}_{{\overline{\mathbf{3}}}_c}$ and $[{\overline{Q}}_2{\overline{Q}}_4{]}_{{\mathbf{3}}_c}$. The $J/\mathrm{\Psi }$-pair resonances recently observed by LHCb are difficult to be accommodated in the CMIM. The broad structure ranging from 6.2 to 6.8 GeV can be described as the ground tetraquark state $[cc][\overline{c}\overline{c}]$ in the various dynamical models. The narrow structure $X(6900)$ can be identified as the excited state $[cc][\overline{c}\overline{c}]$ with $L=1$ ($L=2$) in the constituent quark model (color flux-tube model).

According to the classification of the quark model, the hadrons going beyond three-quark baryon and quark-antiquark meson pictures are called exotic hadrons. Many new hadrons have been observed since 2003, some of which exhibit exotic behaviors. There are a lot of excellent review articles on exotic hadrons available so far; the present article tries to focus on the recent experimental and theoretical progress on the exotic states from the perspective of the quark model. Although lattice quantum chromodynamics may give the final answer of the problem, the phenomenological models are still powerful tools to explore the exotic states and to provide insight on the phenomenology of hadrons. The spatial and color structures of multiquark states and the channel coupling calculation are emphasized through reviewing some bound states, molecular and color structure resonances. Finally, the unquench effects of some exotic states are reviewed. With the accumulation of experimental data on multiquark states and inspiration of underlying theory developments, more reasonable phenomenological models incorporating multi-body interactions and high Fock components to unify the description of normal hadrons and exotic hadrons are expectable.

We make an exhaustive investigation on the pentaquark states $qqqc\overline{c}$ ($q=u$, $d$ and $s$) and discuss the effect of color structures in a multiquark color flux-tube model. We exhibit a novel picture of the structure and properties of the states $P_c$ and $P_{cs}$ observed by the LHCb Collaboration. We can describe the states as the compact pentaquark states in the model. The spin-parity of the group of $P_c(4312{)}^{+}$ and $P_c(4337{)}^{+}$ is ${\frac{1}{2}}^{-}$ while that of the group of $P_c(4380{)}^{+}$, $P_c(4440{)}^{+}$ and $P_c(4457{)}^{+}$ is ${\frac{3}{2}}^{-}$. Their structures are pentagon, diquark, pentagon, diquark, and octet, respectively. The members in each group can be analogically called QCD isomers because of their the same spin-parity and quark content but different color structures. The singlet $P_{cs}(4459{)}^0$ has pentagon structure and spin-parity of ${\frac{1}{2}}^{-}$. In addition, we also predict the $P_{cs}$, $P_{css}$ and $P_{csss}$ families in the model. The five-body confinement potential based on the color flux-tube picture, which is a collective degree of freedom and induces QCD isomer phenomenon, plays an important role in the formation of the compact states.

Within the framework of the color flux-tube model with a multibody confinement potential, we systematically investigate the hidden charmed states observed in recent years. It can be found that most of them can be described as the compact tetraquark states $[cq][\overline{c}\overline{q}]$ ($q=u$, $d$ and $s$) in the color flux-tube model. The multibody confinement potential based on the color flux-tube picture is a dynamical mechanism in the formation and decay of the compact tetraquark states.