We develop techniques to calculate the four Delta electromagnetic form factors using lattice QCD, with particular emphasis on the subdominant electric quadrupole form factor that probes deformation of the Delta. Results are presented for pion masses down to approximately 350 MeV for three cases: quenched QCD, two flavors of dynamical Wilson quarks, and three flavors of quarks described by a mixed action combining domain-wall valence quarks and dynamical staggered sea quarks. The magnetic moment of the Delta is compared with chiral effective field theory calculations and the Delta charge density distributions are discussed.