University of Padova, Italy
In this talk I shall briefly review the most significant steps in the development of subspace algorithms, starting from the seminal papers in the late eighties, through the most widely known procedures (CCA,N4SID, MOESP), ending with most recent algorithms which have allowed subspace identification to be applied with closed loop-data. This shall be done keeping contact with stochastic realization theory. I shall give particular emphasis to a recent body of results on the asymptotic statistical properties of subspace methods which have also allowed to perform comparison between different methods. Some perspectives on future developments and open aspects will be given.