The I-FENN (Integrated Finite Element Neural Network) approach, previously introduced by some of the authors [1,2], is a new computational paradigm for multi-physics problems, which utilizes machine learning based PDE solvers within the Finite Element Method (FEM). I-FENN accelerates the numerical solution of coupled problems by splitting the PDEs into two solvers: mechanical equilibrium is solved via conventional FEM, while physics-related equations are solved through a pre-trained neural network (NN). The two solvers constantly exchange information as in a typical staggered scheme. Thus, numerical accuracy is ensured due to the minimization of the residuals, while computational speedup stems from the swift predicting capabilities of the trained network. The framework has been successfully applied in several multi-physics problems, including non-local gradient damage and thermoelasticity. In this work, we show for the first time how I-FENN can efficiently solve phase-field fracture problems. We first discuss the overarching workflow and we arrive at the system of target PDEs. Then, we present different network training schemes including data-driven and physics-enhanced formulations, and we discuss how each method affects the accuracy of the I-FENN predictions. We examine the accuracy and efficiency of I-FENN against several benchmark problems from the literature, including single- or multiple-crack domains with varying loading setups. Finally, we present an in-depth investigation of I-FENN’s robustness, by examining its convergence rate for different levels of network training quality, and by evaluating its performance against strict convergence criteria.