Handoff is a key element in wireless cellular networks in order to provide quality of service (QoS) to the users and to support users' mobility. Handoff failure will result in the forced termination of an ongoing call. From the user's point of view, the service of a handoff request is more important, as the forced termination of an ongoing call is more annoying than the blocking of new calls. Therefore, in order to support QoS to the users and to provide ubiquitous coverage, the handoff procedure ought to be further investigated. This paper provides a comprehensive survey of the basic elements, the different types and phases of the handoff procedure. Moreover, particular interest has been given in the horizontal handoff execution phase by discussing and classifying the most recent handoff prioritization schemes into categories based on the concepts that these schemes adopt, e.g. channel reservation, handoff queueing, channel transferred, subrating, genetic and hybrid schemes and in the vertical handoff decision phase by presenting different decision algorithms.