We show how successful supersymmetric hybrid inflation is realized in realistic models where the resolution of the minimal supersymmetric standard model µ problem is intimately linked with axion physics. The scalar fields that accompany the axion, such as the saxion, are closely monitored during and after inflation to ensure that the axion isocurvature perturbations lie below the observational limits. The scalar spectral index ns ≃ 0.96 − 0.97, while the tensor-to-scalar ratio r, a canonical measure of gravity waves, lies well below the observable range in our example. The axion domain walls are inflated away, and depending on the axion decay constant fa and the magnitude of the µ parameter, the axions and/or the lightest supersymmetric particle compose the dark matter in the universe. Non-thermal leptogenesis is naturally implemented in this class of models.PACS numbers: 98.80.Cq