Methods and apparatus relating to substructures for three-dimensional objects are described. In an example, a processing apparatus includes: an interface to receive data representing a three-dimensional model object, the data including object model data and object property data; a mapping module to map received data to a print material coverage representation; a halftone module to provide halftone threshold data; and a substructure module to define a substructure for a three-dimensional object to be generated, the substructure specifying in at least a region thereof a consistent lattice structure and a variable material distribution. The apparatus is to apply a substructure and a halftoning to the print material coverage representation to generate control data for the production of a three-dimensional object having the substructure.