We present a system for authoring and viewing interactive cutaway illustrations of complex 3D models using conventions of traditional scientific and technical illustration. Our approach is based on the two key ideas that 1) cuts should respect the geometry of the parts being cut, and 2) cutaway illustrations should support interactive exploration. In our approach, an author instruments a 3D model with auxiliary parameters, which we call "rigging," that define how cutaways of that structure are formed. We provide an authoring interface that automates most of the rigging process. We also provide a viewing interface that allows viewers to explore rigged models using high-level interactions. In particular, the viewer can just select a set of target structures, and the system will automatically generate a cutaway illustration that exposes those parts. We have tested our system on a variety of CAD and anatomical models, and our results demonstrate that our approach can be used to create and view effective interactive cutaway illustrations for a variety of complex objects with little user effort.