A review of the results of the search for four-quark states in $\gamma\gamma$ collisions during the last decade is presented. The resonance phenomena in the reactions $\gamma\gamma\to\rho^0\rho^0$, $\gamma\gamma\to\rho^+\rho^-$, $\gamma\gamma\to\omega\rho^0$, $\gamma\gamma\to\mathbf{K}^*\bar{\mathbf{K}}^*$, $\gamma\gamma\to\omega\omega$, $\gamma\gamma\to\varphi V$, $\gamma\gamma\to\pi^0\eta$ and $\gamma\gamma\to\pi\pi$ are discussed in detail. In particular, it is shown that presently there are telling arguments for observation of a tensor exotic $\mathbf{q}^2\bar{\mathbf{q}}^2$, resonance with isospin $I=2$ near the $\rho\rho$ threshold in $\gamma\gamma\to\rho^0\rho^0$ and $\gamma\gamma\to\rho^+\rho^-$. A set of new experiments for the elucidation of the physical nature of the considered phenomena is also suggested.