Dictionaries are very useful objects for data analysis, as they enable a compact representation of large sets of objects through the combination of atoms. Dictionary-based techniques have also particularly benefited from the recent advances in machine learning, which has allowed for data-driven algorithms to take advantage of the redundancy in the input dataset and discover relations between objects without human supervision or hard-coded rules. Despite the success of dictionary-based techniques on a wide range of tasks in geometric modeling and geometry processing, the literature is missing a principled state-of-the-art of the current knowledge in this field. To fill this gap, we provide in this survey an overview of data-driven dictionary-based methods in geometric modeling. We structure our discussion by application domain: surface reconstruction, compression, and synthesis. Contrary to previous surveys, we place special emphasis on dictionary-based methods suitable for 3D data synthesis, with applications in geometric modeling and design. Our ultimate goal is to enlight the fact that these techniques can be used to combine the data-driven paradigm with design intent to synthesize new plausible objects with minimal human intervention. This is the main motivation to restrict the scope of the present survey to techniques handling point clouds and meshes, making use of dictionaries whose definition depends on the input data, and enabling shape reconstruction or synthesis through the combination of atoms.