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 $J/\psi$) is an example of the second category. The double-scattering mechanisms of two $\rho^0$ meson production is discussed in addition.