Multi-innovation identification is an important branch of system identification.The innovation is the useful information that can improve parameter estimation or state estimation accuracies.This paper discusses various multi-innovation identification methods for linear regression models,including the multi-innovation projection algorithm,the multi-innovation stochastic gradient algorithm,the multi-innovation forgetting gradient algorithm,the interval-varying multi-innovation stochastic gradient algorithm,the multi-innovation least squares algorithm,the interval-varying multi-innovation least squares algorithm,and so on.We give the stochastic gradient algorithm,the multi-innovation stochastic gradient algorithm and the multi-innovation least squares identification algorithm for equation error type systems,output error type systems and input nonlinear systems.Finally,we state that the multi-innovation identification theory can be developed to multi-innovation observer and multi-innovation Kalman filtering theory.