Fracture mechanics is nowadays a consolidated theory within the realm of continuum mechanics, that has been developed starting from the pioneering work of Griffith where the key concepts of energy release rate and fracture toughness (surface energy) has been established. A lacking feature of Griffith's fracture criterion, including its variational extension, is the inability to capture and describe fatigue cracks, that is cracks evolving due to repeated loads that singularly would be too small to cause the material failure. The aim of this contribution is to discuss how to possibly endow Griffith's fracture theory and related phase-field models with the ability to describe fatigue cracks. The proposed idea of the updated model is to consider the fracture toughness not as a material parameter anymore but rather as a material function, assumed to be decreasing as an accumulated energy based measure increases.