Algorithms using multi-step least-squares as an alternative to maximum likelihood and prediction error estimation of rational linear models have been around for than half a century, starting with Durbin’s classical work on MA-models. In this talk we review the different strands of such methods that exist and elucidate on their relations. We also compare these methods with the popular subspace identification approach. We also highlight Weighted Null Space Fitting, the last contribution to this type of algorithms and show some recent results for MIMO and network system identification.