This report contains the complete (expanded) texts of 4 of the five lectures and a 2 page introduction to the remaining lecture delivered at a one day conference on "New trends in filtering and identification of stochastic systems", which took place on Jan. 23, 1980 at Erasmus University Rotterdam. We aimed to present some of the rather striking and very promising new developments especially in recursive and/or nonlinear filtering and as such the meeting was also intended as a preliminary warm-up for the Advanced-Study-Institute "Stochastic Systems: the mathematics of filtering and identification which will take place at Les Arcs (Savoie) this summer (June 22-July 5).