Nanotechnology attracts much attention due to not only its useful engineering applications, but also their superior material performances. As the dimensions of the devices become smaller and smaller, however, understanding the mechanical properties of materials at sub-micron length scales becomes more challenging. This is driven by the knowledge that many mechanical properties at the sub-micron scale differ from those at the macroscopic scale and, in addition, mechanical deformations are coupled with other concurrent physical phenomena, such as diffusion, chemical reaction, and phase transformation. For the reliable design of MEMS or NEMS devices, nanotechnology has always called for an understanding of the mechanical behaviors of materials at small length scales. In the first part of this talk, size dependent plasticity in metallic micropillars will be in terms of dislocation mechanics. Considering dislocation sources from the surface, micropillar plasticity will be analyzed using three dimensional dislocation dynamics model to understand how dislocation behavior relates to mechanical response in metals. In another part of the talk, size-dependent fracture of Si anodes in lithium ion battery will be explored in both crystalline and amorphous structures. Silicon (Si) nanostructures are attractive candidates for Li-ion battery electrodes because they provide both large specific charging capacity and less constraint on the volume changes that occur during Li insertion and extraction. Highlighting the intimate relation between mechanics and electrochemistry, theories of lithiation and accompanying large deformation and fracture will be discussed.