Forgetting is a useful tool for tailoring ontologies by reducing the number of concepts and roles, while preserving sound and complete reasoning. Some attempts have been made to address the problem of forgetting in some relatively simple description logics (DLs) such as DL-Lite and extended EL . Ontologies in those works are mostly expressed as TBoxes rather than general knowledge bases (KBs). However, the issue of forgetting for general KBs in more expressive ontology languages, such as ALC and OWL DL, is largely unexplored. In particular, the problem of characterizing and computing forgetting is still open. In this paper, we first define semantic forgetting about concepts and roles in ALC ontologies and show several important properties of forgetting in this setting. Unlike the case of DL-Lite, the result of forgetting in an ALC ontology may not exist in general, which makes the problem of how to compute forgetting in ALC more challenging. As a result, we tackle the non-existence of the result of forgetting in ALC ontologies by first investigating forgetting in concept descriptions and then defining and studying a series of approximations to the result of forgetting in ALC ontologies. We show that forgetting in ALC ontologies can be approximated through computing forgetting for concept descriptions. Our algorithms can be embedded into an ontology editor to enhance its ability to manage and apply (large) ontologies.