In this paper, we propose a deep learning based approach for facial action unit (AU) detection by enhancing and cropping regions of interest of face images. The approach is implemented by adding two novel nets (a.k.a. layers): the enhancing layers and the cropping layers, to a pretrained convolutional neural network (CNN) model. For the enhancing layers (noted as E-Net), we have designed an attention map based on facial landmark features and apply it to a pretrained neural network to conduct enhanced learning. For the cropping layers (noted as C-Net ), we crop facial regions around the detected landmarks and design individual convolutional layers to learn deeper features for each facial region. We then combine the E-Net and the C-Net to construct a so-called Enhancing and Cropping Net (EAC-Net), which can learn both features enhancing and region cropping functions effectively. The EAC-Net integrates three important elements, i.e., learning transfer, attention coding, and regions of interest processing, making our AU detection approach more efficient and more robust to facial position and orientation changes. Our approach shows a significant performance improvement over the state-of-the-art methods when tested on the BP4D and DISFA AU datasets. The EAC-Net with a slight modification also shows its potentials in estimating accurate AU intensities. We have also studied the performance of the proposed EAC-Net under two very challenging conditions: (1) faces with partial occlusion and (2) faces with large head pose variations. Experimental results show that (1) the EAC-Net learns facial AUs correlation effectively and predicts AUs reliably even with only half of a face being visible, especially for the lower half; (2) Our EAC-Net model also works well under very large head poses, which outperforms significantly a compared baseline approach. It further shows that the EAC-Net works much better without a face frontalization than with face frontalization through image warping as pre-processing, in terms of computational efficiency and AU detection accuracy.