We review lattice vibrational modes in atomically thin two-dimensional (2D) layered materials, focusing on 2D materials beyond graphene, such as group Ⅵ transition metal dichalcogenides, topological insulator bismuth chalcogenides, and black phosphorus. Although the composition and structure of those materials are remarkably different, they share a common and important feature, i.e., their bulk crystals are stacked via van der Waals interactions between "layers" while each layer is comprised of one or more atomic planes. First, we review the background of some 2D materials (MX₂, M = Mo, W; X = S, Se, Te. Bi₂X₃, X = Se, Te. Black phosphorus), including crystalline structures and stacking order. We then review the studies on vibrational modes of layered materials and nanostructures probed by the powerful yet nondestructive Raman spectroscopy technique. Based on studies conducted before 2010, recent investigations using more advanced techniques have pushed the studies of phonon modes in 2D layered materials to the atomically thin regime, down to monolayers. We will classify the recently reported general features into the following categories: phonon confinement effects and electron-phonon coupling, anomalous shifts in high-frequency intralayer vibrational modes and surface effects, reduced dimensionality and lower symmetry, the linear chain model and the substrate effect, stacking orders and interlayer shear modes, polarization dependence, and the resonance effect. Within the seven categories, both intralayer and interlayer vibrational modes will be discussed. The comparison between different materials will be provided as well.