Factorization Machine (FM) is a widely used supervised learning approach by effectively modeling of feature interactions. Despite the successful application of FM and its many deep learning variants, treating every feature interaction fairly may degrade the performance. For example, the interactions of a useless feature may introduce noises; the importance of a feature may also differ when interacting with different features. In this work, we propose a novel model named Interaction-aware Factorization Machine (IFM) by introducing Interaction-Aware Mechanism (IAM), which comprises the feature aspect and the field aspect, to learn flexible interactions on two levels. The feature aspect learns feature interaction importance via an attention network while the field aspect learns the feature interaction effect as a parametric similarity of the feature interaction vector and the corresponding field interaction prototype. IFM introduces more structured control and learns feature interaction importance in a stratified manner, which allows for more leverage in tweaking the interactions on both feature-wise and field-wise levels. Besides, we give a more generalized architecture and propose Interaction-aware Neural Network (INN) and DeepIFM to capture higher-order interactions. To further improve both the performance and efficiency of IFM, a sampling scheme is developed to select interactions based on the field aspect importance. The experimental results from two well-known datasets show the superiority of the proposed models over the state-of-the-art methods.