Fracture mechanics is one of the most challenging and impactful research areas in engineering. The ability to accurately predict fracture phenomena is essential for the safe and efficient design of structural systems, with profound economic, environmental, and societal implications. Preventing structural failure reduces maintenance costs, material losses, environmental hazards associated with catastrophic spills, and the loss of human life. The foundations of modern fracture mechanics can be traced back to the seminal work of Griffith [1], who introduced the energetic interpretation of fracture and the concept of fracture energy associated with crack evolution. Since then, the continuous growth of computational capabilities has driven the development of increasingly sophisticated numerical approaches for fracture analysis. Among these, phase-field methods have emerged as one of the most powerful and versatile frameworks for the simulation of complex fracture processes. Their main strength lies in the ability to represent crack evolution through a continuous description of discontinuous interfaces, naturally handling complex crack topologies without ad-hoc tracking strategies. Within this framework, the accurate modeling of fracture energy dissipation plays a central role. In recent years, high-order phase-field formulations have attracted growing attention due to their enhanced regularity properties and their potential to significantly improve computational efficiency and solution accuracy [2]. The resulting high-order partial differential equations find a particularly suitable discretization environment in Isogeometric Analysis [3], whose high-continuity basis functions provide a natural framework for their numerical treatment. This talk will discuss recent advances in high-order phase-field models for fracture, with particular emphasis on both static and dynamic regimes [4]. Special attention will be devoted to the interplay between variational modeling, numerical efficiency, and predictive capabilities, highlighting how high-order formulations can substantially reduce computational costs while preserving remarkable accuracy in the simulation of complex fracture phenomena.