The past decade has witnessed an enormous rise of two-dimensional layered materials (2DLMs) in the scientific community, including graphene, transition metal dichalcogenides (TMDs), hexagonal boron nitride (hBN), and black phosphorous (bP) etc. The nature of weak van der Waals (vdW) interactions between the atomically thin layers makes it possible to isolation them into few-layer or monolayer form without surface dangling bonds. Remarkable and unique properties appear at the atomically thin limit, and thus opening new opportunities to explore ultra-thin electronic and optoelectronic applications, such as quantum tunneling based devices, ultrafast photodetectors, broadband modulators, solar cells etc. The focuses of this work are developed along two streams: property characterizations of 2DLMs and their novel device explorations. On the characterization front, spectroscopic techniques are utilized for the first time to determine the band offsets of graphene on oxide structures and simultaneously extracting the work function of graphene; using Raman spectroscopy coupled with comprehensive thermal transport modeling, in-plane thermal conductivity in atomically thin TMD monolayers is characterized for the first time. On the device aspect, graphene based terahertz (THz) modulators are invented, promising superior performance; various types of vdW heterojunctions (HJs) are built and tested. For example, vdW Esaki tunneling diodes are demonstrated for the first time, which are subsequently used to build a proof-of-concept radio frequency (RF) oscillator.