A review is given of the dynamic structure of scalar resonances that exhibit a series of features that are unusual for two-quark systems. Recent experimental data on these resonances are analyzed by a very general method that is the most suitable for verifying different assumptions about the dynamic structure of the resonances. It is shown that the four-quark model is the most suitable for describing the known properties of scalar mesons. Attempts to identify any of the known scalar mesons with gluonium are unsuccessful. The phase ambiguity of elastic s-wave $\pi\pi$-scattering and the mixing of the S$^*$ and $\delta^0$ resonances, which are model-independent for scalar resonances, are examined. A number of new experiments that may yield valuable information on the structure of scalar mesons is suggested. In particular, analysis of $\pi\pi\to\mathrm{K}\bar{\mathrm{K}}$ and $\pi\pi\to\pi\pi$ data predicts the appearance of well-defined effects due to the S$^*$ (980) and $\varepsilon$(1400) resonances in the $\pi^+\pi^-\to\eta\eta$ reaction.