Deep neural networks have revolutionized the field of artificial intelligence by enabling machines to learn from data and perform complex tasks with remarkable accuracy. Nevertheless, their “black-box” nature poses a significant challenge for AI safety and interpretability. Mechanistic interpretability, and in particular the study of circuits, aims to address this issue. The field seeks to uncover the computations of neural networks and find meaningful algorithms in the complex systems of neurons and weights. The purpose of this guide is to provide a comprehensive overview of the current state of circuit discovery in neural networks. We explore the historical context, theoretical foundations, and methodologies employed in this field. Furthermore, we summarize key findings from major studies, discuss the practical applications and theoretical advances, and highlight the challenges and limitations encountered in this research. This guide supports new researchers in exploring circuit discovery – a step toward bridging black-box neural networks and human-understandable algorithms, and shaping trustworthy AI.