The remarkable performance of modern AI systems has been driven by unprecedented scales of data, computation, and energy -- far exceeding the resources required by human intelligence. This disparity highlights the need for new guiding principles and motivates drawing inspiration from the fundamental organizational principles of brain computation. Among these principles, modularity has been shown to be critical for supporting the efficient learning and strong generalization abilities consistently exhibited by humans. Furthermore, modularity aligns well with the No Free Lunch Theorem, which highlights the need for problem-specific inductive biases and motivates architectures composed of specialized components that solve subproblems. However, despite its fundamental role in natural intelligence and its demonstrated benefits across a range of seemingly disparate AI subfields, modularity remains relatively underappreciated in mainstream AI research. In this work, we review several research threads in artificial intelligence and neuroscience through a conceptual framework that highlights the central role of modularity in supporting both artificial and natural intelligence. In particular, we examine what computational advantages modularity provides, how it has emerged as a solution across several AI research areas, which modularity principles the brain exploits, and how modularity can help bridge the gap between natural and artificial intelligence.