In this paper, we focus on the template inversion attack against face recognition systems and propose a new method to reconstruct face images from facial templates. Within a generative adversarial network (GAN)-based framework, we learn a mapping from facial templates to the intermediate latent space of a pre-trained face generation network, from which we can generate high-resolution realistic reconstructed face images. We show that our proposed method can be applied in whitebox and blackbox attacks against face recognition systems. Furthermore, we evaluate the transferability of our attack when the adversary uses the reconstructed face image to impersonate the underlying subject in an attack against another face recognition system. Considering the adversary's knowledge and the target face recognition system, we define five different attacks and evaluate the vulnerability of state-of-the-art face recognition systems. Our experiments show that our proposed method achieves high success attack rates in whitebox and blackbox scenarios. Furthermore, the reconstructed face images are transferable and can be used to enter target face recognition systems with a different feature extractor model. We also explore important areas in the reconstructed face images that can fool the target face recognition system.