Hyperelastic adhesives are well known for their capacity of creating lightweight joints with optimised stress distribution. Due to the intrinsically multi-material nature of adhesive joints, i.e. one material for the adhesive, and at least one material for the substrate, the stress distributions within the adhesive layer can be complex. In operational conditions, hyperelastic adhesive joints are exposed to cyclic loads (e.g. vibration), which makes fatigue failure a main concern in the design of bonded structures. For this reason, the development of accurate fatigue failure criteria is a key aspect to ensure safety and avoid over-dimensioning of joints. At the same time, methods that not only provide the service life, i.e. number of cycles to failure, but provide a progressive damage evolution can be very useful within structural health monitoring applications. In this context, the current work presents a comparison between stress-based fatigue failure criteria, namely (i) nominal shear and tensile stresses, (i) the Drucker –Prager criterion (an invariant-based equivalent stress criterion), and (iii) the Findley criterion (a critical plane stress-based criterion). The failure criteria were employed for the lifetime prediction of adhesively bonded joints with varying stress ratio (R=0.1, R=0.5 and R= -1) of butt and thick adherend shear test joints. A method for crack detection based on amplitude compliance is used to define a safety factor for adhesively bonded joints applications. An analytical model based on cumulative damage is applied to capture damage evolution for the adhesively joints and be used for crack instability monitoring.