Content-aware image retargeting has attracted a lot of interests recently. The key and most challenging issue for this task is how to balance the tradeoff between preserving the important contents and minimizing the visual distortions on the consistency of the image structure. In this paper we present a novel filtering-based technique to tackle this issue, called ”importance filtering”. Specifically, we first filter the image saliency guided by the image itself to achieve a structure-consistent importance map. We then use the pixel importance as the key constraint to compute the gradient map of pixel shifts from the original resolution to the target. Finally, we integrate the shift gradient across the image using a weighted filter to construct a smooth shift map and render the target image. The weight is again controlled by the pixel importance. The two filtering processes enforce to maintain the structural consistency and yet preserve the important contents in the target image. Furthermore, the simple nature of filter operations allows highly efficient implementation for real-time applications and easy extension to video retargeting, as the structural constraints from the original image naturally convey the temporal coherence between frames. The effectiveness and efficiency of our importance filtering algorithm are confirmed in extensive experiments.