Parametric face models, such as morphable and blendshape models, have shown great potential in face representation, reconstruction, and animation. However, all these models focus on large-scale facial geometry. Facial details such as wrinkles are not parameterized in these models, impeding accuracy and realism. In this paper, we propose a method to learn a Semantically Disentangled Variational Autoencoder (SDVAE) to parameterize facial details and support independent detail manipulation as an extension of an off-the-shelf large-scale face model. Our method utilizes the non-linear capability of Deep Neural Networks for detail modeling, achieving better accuracy and greater representation power compared with linear models. In order to disentangle the semantic factors of identity, expression and age, we propose to eliminate the correlation between different factors in an adversarial manner. Therefore, wrinkle-level details of various identities, expressions, and ages can be generated and independently controlled by changing latent vectors of our SDVAE. We further leverage our model to reconstruct 3D faces via fitting to facial scans and images. Benefiting from our parametric model, we achieve accurate and robust reconstruction, and the reconstructed details can be easily animated and manipulated. We evaluate our method on practical applications, including scan fitting, image fitting, video tracking, model manipulation, and expression and age animation. Extensive experiments demonstrate that the proposed method can robustly model facial details and achieve better results than alternative methods.