We performed molecular dynamics (MD) simulations of the structure and properties of cerium-containing phosphosilicate, aluminophosphate, and aluminophosphosilicate glasses based on recent spectroscopic data that revealed 95% of cerium ions in such glasses are Ce(3+). New Ce(3+)- and Ce(4+)-O(2-) potentials were developed and used in the MD simulations of these cerium-containing glasses with mixed glass formers. The local environments around cerium ions and network-forming cations, the medium range structure including glass-forming network Q(n) distribution, clustering, and second coordination shell around cerium ions have been carefully characterized. The results showed a longer Ce-O bond length and larger coordination number for Ce(3+) than Ce(4+) (2.48 and 6.4 vs. 2.24 angstrom and 5.8, respectively). Around 5% of Si(4+) ions were found to be in fivefold and sixfold coordination states in cerium phosphosilicate glasses, rather than the usual fourfold in silicate glasses. At the same time, the silicon-oxygen polyhedra were highly polymerized (over 80% of Q(4)) due to the presence of phosphorus oxide. Aluminum ions were found to be coordinated by four-, five-, and six oxygen ions, with an average coordination number of around 4.2. In both oxidation states, cerium ions were found to be preferentially surrounded by phosphorus-oxygen tetrahedra, which form a kind of solvation shell around them. The preference of network-forming cations around cerium ions in the second coordination shell was found to decrease in the sequence phosphorus, aluminum, silicon.