The research of the cognitive radio networks is facing rigorous challenges with the insufficience of the radio spectrum resources and multi-user contention environment.The fundamental principles of the spectrum handoff was elaborated

including the concepts and characteristics of the spectrum handoff

the classification of the proactive and reactive decisions of the spectrum handoff

spectrum handoff process abstract modeling methods

etc.Then five spectrum handoff algorithms based on the probability theory

Markov process

queuing theory

fuzzy logic

fuzzy neural network

were summarized

which were mainly on the ground of mathematic modeling tools.Some significant research findings of each spectrum handoff algorithm in the academic circle were reviewed.Finally

on account of the analysis of the existing algorithms and research achievements

some important problems of imperfect spectrum detection

target channel selection

idle channel dynamic character that were existed in the current research were summarized and the future research direction of the spectrum handoff were predicted.