We present an interior-point algorithm for nonlinear constrained optimization. The novel feature of the algorithm is that it allows the inexact solution of the primal-dual system during every iteration, meaning that iterative linear solvers present a viable and competitive option in large-scale settings. Loose and practical termination conditions for the iterative linear system solve are presented and shown to provide global convergence guarantees under minimal assumptions. We illustrate the practical performance of our approach on large optimization test set collections and model PDE-constrained problems.