Considerable effort has been put into the development of models describing damage and failure of fiber composites. This paper aims at providing an overview of models for intralaminate fracture of continuous fiber-reinforced polymer composites under quasi-static load. The models are grouped into homogeneous ones, those with some effect of inhomogeneity between fibers and the matrix, and fully inhomogeneous ones. Even a world-wide competition was not able to decide for the one and only homogeneous model. Accounting for the inhomogeneity between fibers and the matrix allows being more close to the real behavior on the account of higher computational effort. They suffer, however, from the difficulty to gather reliable material data. In summary, it must be concluded that a fully satisfying solution is not yet available. Consequently, for the time being, a real test remains the authentic way to secure structural strength.