Primordial features are one of the most important extensions of the StandardRecent results from Cosmic Microwave Background (CMB) experiments, in particular the Planck space mission [1,2], have confirmed to high confidence a Standard Model of cosmology in which the Universe is spatially flat, with nearly Gaussian primordial perturbations with a power-law power spectrum which is, close to but not, scale-invariant. These characteristics, together with the observation of super-horizon perturbations via the large-scale temperature-E-mode polarization anti-correlation [3], are all consistent with predictions of the simplest inflationary models [4][5][6], and make possible to distinguish among different inflationary models, and between inflation and alternative-to-inflation models (e.g. [7,8]). In the simplest single-field models of inflation, the inflaton field driving inflation is a canonical scalar field slowly rolling on a smooth potential. While classes of inflationary models and alternative-to-inflation models have been ruled out by available data, future data will make possible to address the next challenges: to seek further evidence for inflation, and to shed light on the physics of inflationary models. There are three complementary routes: primordial non-Gaussianity, which probes the (self)interactions of fields in the primordial Universe; primordial gravity waves, as they leave a signature in the CMB polarization pattern and are directly related to the energy scale of the primordial Universe; and departures from a smooth power spectrum in the form of specific features. In this paper we study the imprints of the latter signals on the large-scale structure of the Universe and make forecasts of their detectability.An important class of beyond-Standard-Model feature signals is the scale-dependent oscillatory signal in the power spectrum of the curvature perturbations. Depending on their natures, these signals provide a variety of valuable information on the physics of the primordial Universe. Broadly speaking, we will study the following several classes of models, their