This work presents a comprehensive and structured taxonomy of available techniques for managing the handover process in mobility architectures. Representative works from the existing literature have been divided into appropriate categories, based on their ability to support horizontal handovers, vertical handovers and multihoming. We describe approaches designed to work on the current Internet (i.e. IPv4-based networks), as well as those that have been devised for the "future" Internet (e.g. IPv6-based networks and extensions). Quantitative measures and qualitative indicators are also presented and used to evaluate and compare the examined approaches. This critical review provides some valuable guidelines and suggestions for designing and developing mobility architectures, including some practical expedients (e.g. those required in the current Internet environment), aimed to cope with the presence of NAT/firewalls and to provide support to legacy systems and several communication protocols working at the application layer.