Traditional object representation schemes are often inadequate for supporting the variety of object manipulation tasks required in a modern solid modeling system. Hybrid schemes try to achieve a higher representative power by embedding the characteristics of several traditional models. The schemes we consider are Modular Boundary Models (MBMs), which describe the boundary of a solid object as the combination of face-abutting object parts represented in a boundary form, PM-Octrees, which are a combination of octrees and boundary representation, and PM-CSG trees, which are essentially octrees whose leaves represent CSG primitives. In particular, we will focus our attention on an MBM, called the Face-to-Face Composition (FFC) model, which also stores interference information useful to perform Boolean operations. We discuss the problems involved in conversion algorithms which operate between traditional models, and we review conversion algorithms on PM-Octrees and PM-CSG trees. We present a new algorithm for boundary evaluation of an FFC model, and discuss the problem of producing an FFC model from a boundary representation.