We perform a next-to-next-to-leading order (NNLO) analysis of nuclear parton distribution functions (nPDFs) using neutral current charged-lepton (ℓ±+nucleus) deeply inelastic scattering (DIS) data and Drell-Yan (DY) cross-section ratios σDYA/σDYA′ for several nuclear targets. We study in detail the parametrizations and the atomic mass (A) dependence of the nuclear PDFs at this order. The present nuclear PDFs global analysis provides us a complete set of nuclear PDFs, fi(A,Z)(x,Q2), with a full functional dependence on x, A, Q2. The uncertainties of the obtained nuclear modification factors for each parton flavour are estimated using the well-known Hessian method. The nuclear charm quark distributions are also added into the analysis. We compare the parametrization results with the available data and the results of other nuclear PDFs groups. We found our nuclear PDFs to be in reasonably good agreement with them. The estimates of errors provided by our global analysis are rather smaller than those of other groups. In general, a very good agreement is achieved. We also briefly review the recent heavy-ion collisions data including the first experimental data from the LHC proton+lead and lead+lead run which can be used in the global fits of nuclear PDFs. We highlight different aspects of the high luminosity Pb–Pb and p–Pb data which have been recorded by the CMS Collaboration.