Inspired by biological neural networks (BNNs), artificial neural networks (ANNs) have achieved great success in revolutionizing a wide range of tasks and scenarios from computer vision (CV) to natural language processing (NLP). Given their powerful representation capabilities, ANNs have also been widely used in the brain science community to represent the organization and dynamics of the human brain from the perspective of BNNs, such as functional brain networks (FBNs). Despite this, the connections between ANNs and BNNs remain largely unexplored due to the lack of effective tools to bridge and connect two different domains, i.e., the brain and artificial intelligence. Furthermore, how to leverage the prior knowledge of BNNs to inspire the design of ANNs and boost their performance is still an open question. To overcome these challenges, we proposed a series of computational frameworks to bridge the gap mentioned above. Our approaches involve exploring the hierarchical organization of brain activities, representing the brain structure and function as embeddings, connecting them with ANNs to couple the semantics of two domains, and utilizing the prior knowledge from the human brain to inspire and guide the design of ANNs. Extensive experiments demonstrated that the proposed computational frameworks could effectively explore the connection between ANNs and BNNs, yielding neuroscientifically meaningful interpretations. Additionally, our brain-inspired design of ANNs, informed by prior knowledge from human brains, achieved comparable and state-of-the-art performances in several tasks. Overall, this study provides novel insights from brains toward brain-inspired artificial intelligence.