Multiresolution models with different levels of detail are a basic tool for handling very large and complex systems in computer aided design applications such as ship design. In this work, we discuss several automatic simplification algorithms that generate a multiresolution family of solid models that approximate with different levels of detail the boundary representation of a given polyhedral solid. Methods based on the simplification of triangular meshes are discussed together with octree based algorithms. Comparison criteria include the possibility of geometry and topology simplification, the availability of approximation bounds and feature preservation.