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Fatigue-induced damage is still one of the most uncertain failures in structural systems. Prognostic health monitoring together with surrogate models can help to predict the fatigue life of a structure. This paper demonstrates how to combine data from previously observed crack evolutions with data from the currently observed structure in order to predict crack growth and the total fatigue life. We show the application of one physics-based model, which is based on Paris' law, and four mathematical surrogate models: recurrent neural networks, Gaussian process regression, k-nearest neighbors, and support vector regression. For a coupon test, we predict the time to failure and the crack growth with confidence intervals. Moreover, we compare the performance of all proposed models by the mean absolute error, coefficient of determination, mean of log-likelihood, and their confidence intervals. The results show that the best mathematical surrogate models are Gaussian process regression and recurrent neural networks. Furthermore, this paper shows that the mathematical surrogate models tend to have conservative confidence intervals, whereas the physics-based model exhibits overly optimistic (too small) confidence intervals.