This chapter, authored by Blaise Bourdin, Gilles A. Francfort, and Jean-Jacques Marigo, provides an extensive overview of the variational approach to brittle fracture. The authors revisit and extend Griffith's classic energy-based theory of crack propagation, using modern tools from the Calculus of Variations. They compare and contrast the merits of different surface energy models, emphasizing the importance of cohesiveness at crack surfaces as introduced by Barenblatt. The chapter covers both theoretical and computational aspects, including examples from simple test settings and numerical simulations. It also discusses the extension of the model to fatigue and rate-independent processes. The authors aim to provide a comprehensive and incisive treatment of the variational structure of fracture, highlighting the challenges and advancements in the field. The chapter is structured into several sections, each delving into specific aspects of the variational approach, such as initiation, propagation, irreversibility, and numerical implementation.This chapter, authored by Blaise Bourdin, Gilles A. Francfort, and Jean-Jacques Marigo, provides an extensive overview of the variational approach to brittle fracture. The authors revisit and extend Griffith's classic energy-based theory of crack propagation, using modern tools from the Calculus of Variations. They compare and contrast the merits of different surface energy models, emphasizing the importance of cohesiveness at crack surfaces as introduced by Barenblatt. The chapter covers both theoretical and computational aspects, including examples from simple test settings and numerical simulations. It also discusses the extension of the model to fatigue and rate-independent processes. The authors aim to provide a comprehensive and incisive treatment of the variational structure of fracture, highlighting the challenges and advancements in the field. The chapter is structured into several sections, each delving into specific aspects of the variational approach, such as initiation, propagation, irreversibility, and numerical implementation.