Two-dimensional (2D) materials have attracted immense attention due to their novel and exceptional characteristics such as atomically thin body, large surface area to volume ratio, unique electronic properties, and high charge carrier mobilities. This makes 2D materials promising candidates for the next generation of low-power, high-performance electronic devices. In this thesis, the mechanical, vibrational, thermal, and electronic properties of several 2D materials are explored and their possible application to devices is examined. The work was carried out in collaboration with experimentalists at several institutions with theoretical calculations confirming experimental measurements and improving the understanding of the observed results.