This thesis is concerned with modeling geometric patterns. Specifically, a clear and practical definition for regular patterns is proposed. Based on this definition, this thesis proposes the following modeling setting to describe the semantic transfer of a model between various forms of pattern regularity: (1) recognition or identification of patterns in digital models of 3D assemblies and scenes, (2) pattern regularization, (3) pattern modification and editing by varying the repetition parameters, and (4) establishing exceptions (designed irregularities) in regular patterns. In line with this setting, this thesis describes a representation and approach for designing and editing hierarchical assemblies based on grouped, nested, and recursively nested patterns. Based on this representation, this thesis presents the OCTOR approach for specifying, recording, and producing exceptions in regular patterns. To support editing of free-form shape patterns on surfaces, this thesis also presents the imprint-mapping approach which can be used to identify, extract, process, and apply relief features on surfaces. Pattern regularization, modification, and exceptions are addressed for the case of relief features on surfaces.