Caldarelli received his Ph.D. from SISSA, after which he was a postdoc in the Department of Physics and School of Biology, University of Manchester. He then worked at the Theory of Condensed Matter Group, University of Cambridge, where he worked with Robin Ball and stayed in Wolfson College. He returned to Italy as a lecturer at National Institute for Condensed Matter (INFM) and later as Primo Ricercatore in the Institute of Complex Systems of the National Research Council of Italy. In this period he was also the coordinator of the Networks subproject, part of the Complexity Project, for the Fermi Centre. He also spent some terms at University of Fribourg (Switzerland) and in 2006 he has been visiting professor at École Normale Supérieure in Paris.