We propose a novel method for detecting mesh saliency, a perceptually-based measure of the importance of a local region on a 3D surface mesh. Our method incorporates <i>global</i> considerations by making use of spectral attributes of the mesh, unlike most existing methods which are typically based on <i>local</i> geometric cues. We first consider the properties of the log-Laplacian spectrum of the mesh. Those frequencies which show differences from expected behaviour capture saliency in the frequency domain. Information about these frequencies is considered in the spatial domain at multiple spatial scales to localise the salient features and give the final salient areas. The effectiveness and robustness of our approach are demonstrated by comparisons to previous approaches on a range of test models. The benefits of the proposed method are further evaluated in applications such as mesh simplification, mesh segmentation, and scan integration, where we show how incorporating mesh saliency can provide improved results.