Nanowires are among the most exciting one-dimensional nanomaterials because of their unique properties, which result primarily from their chemical composition and large surface area to volume ratio. These properties make them ideal building blocks for the development of next generation electronics, opto-electronics, and sensor systems. In this article, we focus on the unique mechanical properties of nanowires, which emerge from surface atoms having different electron densities and fewer bonding neighbors than atoms lying within the nanowire bulk. In this respect, atomistic simulations have revealed a plethora of novel surface-driven mechanical behavior and properties, including both increases and decreases in elastic stiffness, phase transformations, shape memory, and pseudoelastic effects. This article reviews such atomistic simulations, as well as experimental data of these phenomena, while assessing future challenges and directions.