\indent Multicomponent vesicle adhesion and fusion play important roles in many biological processes such as exocytosis, endocytosis. Many experimental and theoretical studies have focus on this subject. In this talk, we will first briefly review the biological background of the lipid bilayer vesicle membranes and the existing works on modeling the vesicle membranes, mainly the sharp interface model and the diffuse interface model. we will then consider the adhesion of multicomponent vesicle membranes. By using geometric description (sharp interface model) to represent the vesicle surface, and a phase field labeling function to distinguish the different components on the vesicle, the total energy, governing the equilibrium shapes of the vesicle, is set up. By solving the Euler-Lagrange equations, we present a number of typical adhered axisymmetric two-component vesicle profiles. A numerical experiment is conducted to show that adhesion may promote phase separation for a multicomponent vesicle. Thirdly, vesicle-vesicle adhesion and fusion process are discussed. By incorporating the adhesion effect, we mainly focus on the prefusion and postfusion states in the fusion process. Numerical experiments reveal that there can be many interesting equilibrium configurations of the prefusion and postfusion states. By carrying our simulations based on the gradient flow of the associated energy functional, we are also able to elucidate the dynamic transitions between the prefusion and postfusion states.