Coupled identification is an important branch of system identification and is a new identification concept which is used mainly to study identification problems of linear and nonlinear multivariable systems with complex structures and parameter coupling.The auxiliary model identification idea,the multi-innovation identification theory,the hierarchical identification principle,and the coupled identification concept are new identification research ideas,concepts and methods and can be used to study identification problems of systems with unknown process variables,to improve the convergence rates and accuracies of identification methods,to solve identification problems of large-scale multivariable systems with complex structures and of multivariable systems with parameter coupling,reducing the computational load of the identification algorithms.This paper introduces the coupled identification concept of multivariable systems,discusses the(full) coupled least squares identification methods,the(full) coupled stochastic gradient identification methods,the partially coupled stochastic gradient identification methods,the partially coupled least squares identification methods etc for multivariable systems.Finally,we show that the coupled identification methods can be applied to multivariable systems with colored noises,list some model structures of some multivariable systems,and indicate that the coupled identification concept can combine the auxiliary model identification idea,the multi-innovation identification theory,the hierarchical identification principle,the iterative search principle(the gradient iteration,the least squares iteration,the Newton iteration) to study identification problems of linear and nonlinear multivariable systems with colored noises.