This paper gives a survey on recent developments of logical networks and some related systems,including the background of logical networks,the theory of semi-tensor product (STP) of matrices,some fundamental works on logical networks,and some recent related works.In particular,some very recent interesting works for the past ten years are presented,concerning the topics of controllability,observability,stability and stabilization,synchronization,optimal control,disturbance decoupling,and so on.Since the method of STP has great potential in dealing with logical networks and some other related systems,a great attraction from domestic and oversea researchers has been paid on the study of STP and its applications.Some recent important research areas are also surveyed in this paper including pinning control,function perturbations,system decomposition,output tracking issues,symbolic dynamics,and so on.The main objective is to give a comprehensive introduction to the application of STP on logical networks and some other systems.