For the three-year duration of their studies, graduate students can be supported by grants that currently amout to about 1200 Euros per month (free of taxes, fees are waived). The details are given in the Call for Admission.
Scholarships are granted from the Ministry of Instruction, University and Research (MIUR), from Politecnico, from companies, or from the Department, also based on research project funds. The number of available scholarships may change from year to year, but ranges between 50 and 60.
Politecnico di Milano offers Student Aid Benefits and grants for students enrolled in PhD programmes, also to support those that do not have a scholarship. Details for application are available here.