Cell membranes show complex phase behavior due to various interactions between its components such as lipids, sterols and proteins. It is found in recent decades that the plasma membrane is heterogeneous and consists of many stable spatially separated lipid microdomains. These domains are specialized for biological functions such as signal transduction, molecular recognition and cellular adhesion. However, their formation mechanism remains in hot debate. To figure out possible explanations of such complex behavior and further study the properties of similar systems composed of rod-like particles (i.e. liquid crystals), both theoretical models and computer simulation methods are developed. With a combination of theoretical and numerical approach, we can gain a deep understanding of the shape and texture of domains embeded in membrane or other kind of surfaces.