Graphene, a two-dimensional form of carbon with honeycomb lattice structure, exhibits many fascinating physical properties that involve new science and have promise for a number of technological applications. Central to these properties of graphene are its low energy electrons that (a) effectively follow the dynamics of massless Dirac fermions with laws of relativistic quantum mechanics, and (b) couple strongly with certain phonons and external fields. Secondly, a very high stiffness of carbon bonds is responsible for its high in-plane elastic moduli making it useful in composites with ultra-high strength. After reviewing the fundamental physics of graphene, its nano-scale forms and exotic properties, we show how it can be characterized and used in applications like electronic devices, sensors, energy storage and composites. Of late, 2-dimensional MoS2 and related materials have emerged as another class of 2-D materials exhibiting remarkable properties. In contrast to the vanishing electronic band gap in graphene, these materials are semiconductors with a moderate gap and readily suitable for use in electronic devices. Using first-principles and Landau theories, we predict emergence of ferroelectricity in 1T form MoS2 at a metal-semiconductor transition that arises from a strong coupling between its electrons and phonons, making it the world's thinnest known ferroelectric. Based on the strongly coupled dipoles and electrons, we propose a new class of "dipolectronic" devices based on MoS2.