The foundation of the connectionist framework stems from connectionism, which simulates the information processing and learning process of the brain through artificial neural networks. Took an overview on the framework, we introduce connectionist learning theories, including Hebb theory, parallel distributed processing, connectionist models, and neural network theory. Next, we explain some units in neural networks, including biological neuron, artificial neuron, spike neuron, long short-term memory (LSTM) unit, gated recurrent unit (GRU), and capsule unit. Then, we discuss the structures of neural networks, namely, feedforward, feedback, and symmetric neural networks. After that, we introduce the optimizations of neural networks, such as backpropagation, evolutionary methods, and weight-agnostic methods without training the neural networks. Finally, the single- and multiagent networks are also explained with two case studies.