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We discuss diphoton semi(exclusive) production in ultraperipheral lead-leadcollisions at energy of $\sqrt{s_{NN}}$ = 5.5 TeV (LHC) and in proton-protoncollisions at $\sqrt{s_{pp}}$ = 7 TeV (LHC) and $\sqrt{s_{pp}}$ = 100 TeV(FCC). The nuclear calculations are based on equivalent photon approximation inthe impact parameter space. The cross sections for elementary $\gamma\gamma \to\gamma\gamma$ subprocess are calculated including three different mechanisms:box diagrams with leptons and quarks in the loops, a VDM-Regge contributionwith virtual intermediate hadronic excitations of the photons and the two-gluonexchange contribution. We get relatively high cross sections in heavy ioncollisions. This opens a possibility to study the light-by-light (quasi)elasticscattering at the LHC. We find that the cross section for elastic$\gamma\gamma$ scattering could be measured in the lead-lead collisions for thediphoton invariant mass up to $W_{\gamma\gamma} \approx$ 15 - 20 GeV. OurStandard Model predictions are compared to a recent ATLAS experimental result.We present differential distributions for PbPb$\to$PbPb$\gamma\gamma$ andpp$\to$pp$\gamma\gamma$ reaction.

$\gamma\gamma \to \gamma \gamma$ scattering in ultrarelativistic UPC