Neutral pion and $\eta$-meson production in pp, p-A and A-A collisions at LHC energies measured with the ALICE experiment is reviewed. In pp collisions the measured invariant production cross-section both of $\pi^0$ and $\eta$-mesons is reproduced by
Pythia 8 Monash tune while NLO pQCD calculations predict significantly higher yield. The multiplicity dependence of neutral meson
production in p-Pb collisions strongly depends on the rapidity gap between the measured particles and the multiplicity estimator. Nuclear modification factors $Q_{\rm pA}$ of neutral mesons and D-mesons in these collisions are close in all centralities. Neutral meson production in Pb-Pb collisions shows close nuclear modification factors for two energies, $\sqrt{s_{\rm NN}}=2.76$ and 5.02 TeV. Suppression of neutral pions and D-mesons is similar at high $p_{\rm T}>10$ GeV/$c$, while at lower $p_{\rm T}$ D-mesons show smaller suppression.