Connectionism is an approach to understanding the mechanisms of human cognition using simulated networks of neuron-like processing units. In this article, I attempt to report on recent progress in connectionist models that simulate empirical data of natural cognitive tasks, these being visual word perception, memory, word naming, understanding word meanings, speech perception and production, sentence understanding, and reasoning. I also summarize the advantages and disadvantages of these connectionist models. In particular, the problems of dealing with structured information in distributed form, and doing tasks that require variable binding in connectionist networks are discussed from several different perspectives. I argue that connectionist computer simulation offers significant benefits for today's researches of cognitive science, and that connectionist modeling is likely to have an important influence on future studies. The question of how the human brain efficiently realizes and learns symbols and rules by the parallel distributed processing is still one of the great intellectual problems of our time.