Inspired by the beauty of various materials with distinct structures and functions in nature, researchers have been dedicating themselves to discover new ways of creating functional artificial materials to fulfill the increasingly various needs in life. Self-assembly, categorized into the "bottom-up" method, is an important approach in building man-made crystals. However, the self-assembly process itself has not yet been fully understood, both thermodynamically and dynamically. Three major challenges in this field are: 1) given a set of conditions and parameters of the system, what is the equilibrium assembly structure? 2) given a predetermined structure, how should we design particles to self-assemble it? 3) how to avoid possible kinetic barriers to assembly equilibrium structures? Here we try to answer some of the above questions using statistical mechanics approaches and then provide some guidance to colloidal experiments. More specifically, we first study a quasi-two-dimensional, binary colloidal alloy that exhibits liquid-solid and solid-solid phase transitions, focusing on the kinetics of a diffusionless transformation between two crystal phases. And then we study the densest packing structures and assembly processes of hard spheres in a cylinder. We also try to experimentally realize this system by focusing nano-particles in a standing acoustic wave (SAW). Although it is found to be very difficult to assembly nano-particles by SAW, we identify the experimental limitations of this method.