Optimizing compilers for object-oriented languages apply static class analysis and other techniques to try to deduce precise information about the possible classes of the receivers of messages; if successful, dynamicallydispatched messages can be replaced with direct procedure calls and potentially further optimized through inline-expansion. By examining the complete inheritance graph of a program, which we call class hierarchy analysis, the compiler can improve the quality of static class information and thereby improve run-time performance. In this paper we present class hierarchy analysis and describe techniques for implementing this analysis effectively in both statically- and dynamically-typed languages and also in the presence of multi-methods. We also discuss how class hierarchy analysis can be supported in an interactive programming environment and, to some extent, in the presence of separate compilation. Finally, we assess the bottom-line performance improvement due to class h...