Active appearance models (AAMs) are generative models of shape and appearance that have proven very attractive for their ability to handle wide changes in illumination, pose, and occlusion when trained in the wild, while not requiring large training data set like regression-based or deep learning methods. The problem of fitting an AAM is usually formulated as a non-linear least squares one and the main way of solving it is a standard Gauss-Newton algorithm. In this paper, we extend AAMs in two ways: we first extend the Gauss-Newton framework by formulating a bidirectional fitting method that deforms both the image and the template to fit a new instance. We then formulate a second order method by deriving an efficient Newton method for AAMs fitting. We derive both methods in a unified framework for two types of AAMs, holistic and part-based, and additionally show how to exploit the structure in the problem to derive fast yet exact solutions. We perform a thorough evaluation of all algorithms on three challenging and recently annotated in-the-wild data sets, and investigate fitting accuracy, convergence properties, and the influence of noise in the initialization. We compare our proposed methods to other algorithms and show that they yield state-of-the-art results, out-performing other methods while having superior convergence properties.