With parametric computer-aided design (CAD) software, designers can create geometric models that are easily updated (within limits) by modifying the values of controlling parameters. These numeric and non-numeric parameters control the geometry in two ways: parametric operations and geometric constraint solving. This paper examines the advances over the last decade in the representation of parametric operations and of solving geometric constraint problems. An extensive literature has grown up surrounding geometric constraint solving and there has been substantial progress in the types of objects and constraints that can be handled robustly. Yet parametric operations have remained largely within the same conceptualization and begin to limit the flexibility of CAD systems, since they still do not align well with a systematic design process.