These networks generally operate in two different modes, viz., supervised and unsupervised modes. The supervised mode of operation requires a supervisor to train the network with a training set of data. Networks operating in unsupervised mode apply topology preservation techniques so as to learn inputs. Representative examples of networks following either of these two modes are presented with reference to their topologies, configurations, types of input-output data and functional characteristics. Recent trends in this computing paradigm are also reported with due regards to the application perspectives.