Various addressing schemes making use of segment tables are examined. The inadequacies of these schemes when dealing with shared addresses are explained. These inadequacies are traced to the lack of an efficient absolute address for objects in these systems. The direct use of a capability as an address is shown to overcome these difficulties because it provides the needed absolute address. Implementation of capability-based addressing is discussed. It is predicted that the use of tags to identify capabilities will dominate. A hardware address translation scheme which never requires the modification of the representation of capabilities is suggested. The scheme uses a main memory hash table for obtaining a segment's location in main memory given its unique code. The hash table is avoided for recently accessed segments by means of a set of associative registers. A computer using capability-based addressing may be substantially superior to present systems on the basis of protection, simplicity of programming conventions, and efficient implementation.