  In the last ten years, the phase-field method has gained much attention as a
novel method to simulate fracture due to its straightforward way allowing to
cover crack initiation and propagation without additional conditions. More
recently, it has also been applied to fatigue fracture due to cyclic loading.
This publication gives an overview of the main phase-field fatigue models
published to date. We present all models in a unified variational framework for
best comparability. Subsequently, the models are compared regarding their most
important features. It becomes apparent that they can be classified in mainly
two categories according to the way fatigue is implemented in the model - that
is as a gradual degradation of the fracture toughness or with an additional
term in the crack driving force. We aim to provide a helpful guide for choosing
the appropriate model for different applications and for developing existing
models further.
