The modern debate around scientific structuralism has revealed the need to reassess the standing and role of both structure and objects in the metaphysics of physics. Ontic structural realism recommends that metaphysics be purged of objects. Nonetheless, its proponents have failed to specify what it means for properties to be relational and structural, and, consequently, to show how the elementary objects postulated by our best theories can be re-conceptualized in structural terms or altogether eliminated. In this chapter, I draw from modern physics in order to untangle various types of relational properties and propose conditions that should be fulfilled for properties to be characterized as structural properties.