Recent theoretical results for electromagnetically induced ultraperipheral reactions of heavy ions

We briefly review our works on ultraperipheral heavy ion collisions. We discuss both $\gamma \gamma$ and rescattering of hadronic photon fluctuation induced by one nucleus in the collision partner. Production of one and two leptonic and pionic and $p\bar{p}$ pairs is discussed as an example of photon-photon processes. The production of single vector mesons (${\rho }^0$ or $J\mathrm{/}\psi$) is an example of the second category. The double-scattering mechanisms of two ${\rho }^0$ meson production is discussed in addition.