In this paper, the notion of simultaneous universality is introduced, concerning operators having orbits that simultaneously approximate any given vector. This notion is related to the well known concepts of universality and disjoint universality. Several criteria are provided, and several applications to specific operators or sequences of operators are performed, mainly in the setting of sequence spaces or spaces of holomorphic functions.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Economía y CompetitividadDeutsche Forschungsgemeinschaf
