We discuss diphoton semi(exclusive) production in ultraperipheral
lead-lead collisions at energy of $\sqrt{s_{NN}}$ = 5.5 TeV (LHC)
and in proton-proton collisions at $\sqrt{s_{pp}}$ = 7 TeV (LHC)
and $\sqrt{s_{pp}}$ = 100 TeV (FCC).
The nuclear calculations are based on equivalent photon approximation
in the 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 contribution with virtual intermediate hadronic excitations
of the photons and the two-gluon exchange contribution.
We get relatively high cross sections in heavy ion collisions.
This opens a possibility to study the light-by-light
(quasi)elastic scattering at the LHC.
We find that the cross section for elastic $\gamma\gamma$ scattering
could be measured in the lead-lead collisions for the diphoton invariant
mass up to $W_{\gamma\gamma} \approx$ 15 - 20 GeV.
Our Standard Model predictions are compared to a recent ATLAS
experimental result.
We present differential distributions for PbPb$\to$PbPb$\gamma\gamma$
and pp$\to$pp$\gamma\gamma$ reaction.